science_objectives_dump.tex

\subsection{Science Objectives}
\label{sec:science}

\vspace{-0.05in}
 
\subsubsection{The Primordial Universe and Cosmic Inflation}

\vspace{-0.05in}

The observed temperature and E-mode polarization of the \ac{CMB} require primordial inhomogeneities in the 
gravitational potential, providing a remarkable observational link to the dynamics of the Universe near the big bang.
Inflation~\cite{guth81,linde82,albrecht82,sato81,kolb94}, a primordial era of accelerated expansion, provides a compelling 
dynamical origin for the observed statistical homogeneity of the primordial perturbations on all spatial scales. 
But, Inflation also predicts an as yet unobserved spectrum of primordial gravitational waves sourced directly by 
quantum fluctuations of the tensor component of the metric. These gravitational waves make a distinct B-mode imprint on the polarization of the \ac{CMB}. 
Any detection of B-mode polarization, whether generated by the primordial gravitational waves of 
Inflation~\cite{kamionkowski97a,zaldarriaga97} or by any other source of early time vector or tensor perturbations, 
would reveal completely new information about the primordial era. The results would provide significant constraints 
and consistency checks for current models or could perhaps even overturn them. A detection would have 
implications for fundamental physics by providing evidence for a new energy scale near the GUT scale. 
In the context of Inflation, the relationship is particularly clear: the 
potential energy $V$ of the inflaton is related to the tensor-to-scalar ratio $r$ at the peak of the 
spectrum by $V^{1/4} = 3.7 \times 10^{16} \ r^{1/4}\,\, {\rm GeV}$. 

Figure~\ref{fig:clall} shows current data, B-modes from vacuum fluctuations of the metric during an Inflationary 
era for two values of $r$, as well as forecasts for the determination of the \ac{CMB} spectra for EPIC-IM. For testing inflation, the largest scales $\ell \leq 10$ are particularly important because they reveal 
the presence of B mode correlations on scales that were super-horizon at the time of recombination~\cite{Lee:2014cya}, 
and because the signal is strongest relative to the B-mode from lensing. A satellite is by far the most suitable 
platform to making the all sky observations necessary to reach the lowest $\ell$'s. In its recent report New Worlds New Horizons (NWNH), the decadal survey committee 
strongly endorsed searches for the B-mode signal from inflation saying that ``The convincing detection of 
B-mode polarization in the CMB produced in the epoch of reionization would represent a watershed discovery.''~\cite{blandford2010}. 
\vspace{-0.1in}
\begin{figure}[ht!]
\begin{center}
\includegraphics[width=3in]{figs/cmb_powspec_v1.pdf}  
\includegraphics[width=3in]{figs/cmbbb_powspec_v1.pdf}
\end{center}
\vspace{-0.25in}
\caption{ \small \setlength{\baselineskip}{0.95\baselineskip}
Predicted determination of the \ac{CMB} power spectra for EPIC-IM (grey boxes) overlaid
on theoretical predictions (solid lines) and including Planck measurements of the 
temperature and E modes (blue) and of several ground-based measurements 
of the lensing B-modes.  The tensor B-mode predictions (blue) are shown 
for two representative values of the tensor-to-scalar
ratio: $r=0.001$ and $r=0.05.$ 
\label{fig:clall} }
\vspace{-0.05in}
\end{figure}

In slow roll Inflation there are just two observationally viable classes of models that naturally explain the measured value of the spectral index $n_s$. 
One is the set of potentials $V(\phi)\propto\phi^p$, which contains many of the canonical inflation models. This 
set is already under significant observational pressure. If the error bars on the spectral index tighten by a factor of about 2, 
and the 95\% C.L. upper limit on $r$ is pushed to even $\sim0.01$, all such models would be ruled out. 
The other class of models includes Starobinsky and Higgs inflation, which both have $r\sim0.003$. A future mission 
capable of reaching $\sigma_r\sim\mathcal{O}(10^{-4})$ would provide significant constraints on nearly every currently favored 
inflation model. The EPIC-IM configuration is forecasted to achieve \textcolor{red}{Raphael will update the following to match figures} $\sigma(r)\sim4.8 \times 10^{-4}$ assuming $r=0.01$ 
and no foregrounds.
\begin{figure}[ht!]
\hspace{-0.2in}
\parbox{4.in}{\centerline {
\includegraphics[width=4.5in]{figs/nsrlabeledrp01v1} } }
\hspace{-0.05in}
%\end{center}
\parbox{2.5in}{
\caption{ \small \setlength{\baselineskip}{0.95\baselineskip}
Forecasted constraints in the $n_{\rm s}$--$r$ plane for a fiducial model with $r=0.01$ for EPIC-IM together 
with the current measured 1 and 2$\sigma$ constraints (blue) ~\cite{Array:2015xqh}. Also shown are predictions 
for the models of the inflaton potential discussed in the text: Chaotic inflation for a range of $N_\star$ values (blue lines); 
Higgs and $R^2$ (large and small dots, respectively);  quartic hilltop (green band); and a sub-class of $\alpha$-attractor
models~\cite{Kallosh:2013hoa}
\label{fig:nsrp01} } }
\vspace{-0.1in}
\end{figure}

A detection of $B$-modes consistent with a primordial spectrum of vacuum fluctuations would be the first observation 
of a phenomena directly related to quantum gravity. In addition, any detection with a next generation satellite would be 
evidence for {\it large-field} Inflation~\cite{Lyth:1996im}, in which a smooth potential that supports Inflation extends over 
a distance in field space $\Delta\phi \gtrsim M_p$. Quantum gravity studies of inflation give a generic 
expectation $\Delta\phi \lesssim M_p$~\cite{Banks:2003sx,Baumann:2014nda,Brown:2015iha,Rudelius:2015xta}, although 
there are some mechanisms to realize large-field inflation \cite{Silverstein:2008sg,Kaloper:2008fb,Marchesano:2014mla,Blumenhagen:2015xpa}. 
A detection of $r$ would therefore provide strong 
motivation to better understand how large-field inflation can be naturally incorporated into quantum gravity. 

All inflation models predict a B-mode spectrum with the shape shown in Figure \ref{fig:clall}, but inflation 
need not be correct \cite{Khoury:2001bz,Brandenberger:2012zb,Ijjas:2015hcc} and does not preclude additional sources of $B$-mode polarization either during or after 
inflation. To be confident of the implications of a detection, the shape and Gaussianity of the B-mode spectrum 
must be characterized. The vast majority of inflation scenarios predict an extremely Gaussian and nearly scale-invariant spectrum for 
gravitational waves. A future satellite mission, combined with currently funded ground-based observations, 
could target $\sigma(n_{\rm t})\lesssim1$ at $r=0.01$, for example, to rule out non-vacuum 
inflationary sources~\cite{Namba:2015gja,Peloso:2016gqs} and physics completely inconsistent with inflation. 

Deeper mapping of $E$-mode polarization will also contribute to testing inflationary models. Large scale $E$-modes will 
provide new tests of isotropy, a prediction of most models of Inflation;  
for example, the observations can reject at 99\% confidence models in which low multipoles are aligned in the temperature maps~\cite{Dvorkin:2007jp}. 
Together with continued improvements at high $\ell$ from the ground, these modes will also improve constraints on the scalar 
spectral index and its changes with scale by factors of about two.  

\begin{figure}[ht!]
\hspace{-0.2in}
\parbox{4.0in}{\centerline {
\includegraphics[width=3.0in]{Figures/probe_spectral_foregrounds_v3.pdf} } }
\hspace{-0.05in}
\parbox{2.5in}{
\caption{ \small \setlength{\baselineskip}{0.95\baselineskip}
Anticipated $y$ and $\mu$ spectral distortions (solid), the signature of resonant recombination lines (solid), and anticipated foreground 
signal levels relevant for spectral distortion measurements (grey bands). 
The simplest extension of a proposed
Explorer class mission (Probe, dash grey) gives approximately 10 times the Explorer sensitivity (PIXIE). 
A better optimized Probe may give detections of all anticipated distortions. 
\label{fig:distortions} } }
\vspace{-0.1in}
\end{figure}

Spectral distortion measurements give additional tests of Inflation. The dissipation of small-scale 
perturbations through Silk-damping leads to $\mu$-distortions~\cite{Sunyaev1970diss, Daly1991, Hu1994, Chluba2012}. 
In $\Lambda$CDM the distortions are predicted at a level of $\mu=(2.0\pm0.14)\times 10^{-8}$, a level that 
is readily accessible to a Probe class mission, see Fig.~\ref{fig:distortions}~\cite{Chluba2012, Chluba2016LCDM}. 

\comred{Jens, is the next paragraph related to inflation, or to basic physics}
A better optimized probe may also give the sensitivity to detect the cosmological recombination 
radiation imprinted by the recombination of hydrogen and helium 
at redshift $z\simeq 10^3-10^4$, which are a probe of the physics of recombination; 
see Fig.~\ref{fig:distortions}~\citep{Sunyaev2009, Chluba2016}. 


%in the CMB spectrum, which provide a unique means to place stringent constraints on the amplitude of the small-scale curvature power spectrum. This information is on small scales (wavelength $0.1 \,{\rm kpc} \lesssim \lambda \lesssim 1\, {\rm Mpc}$) and from early times ($10^4 \lesssim z\lesssim 10^6$), inaccessible through any other observation. 

%In $\Lambda$CDM \citep{Chluba2012, Chluba2016LCDM}, distortions are predicted at a level of $\mu=(2.0\pm0.14)\times 10^{-8}$ (see Fig.~\ref{fig:distortions}). A detection would deliver a complementary test for the inflation paradigm~\citep{Chluba2012inflaton, Dent2012, Chluba2013PCA, Clesse2014, Cabass2016}, and new probes of the particle spectrum of inflation through new tests of non-Gaussianity~\citep{Pajer2012, Ganc2012, Biagetti2013, Razi2015, Chluba2016ng}. 
%It would also bring us to the sensitivity level required to detect the cosmological recombination radiation \citep{Sunyaev2009, Chluba2016} imprinted by the recombination of hydrogen and helium at redshift $z\simeq 10^3-10^4$, which can be used to probe the physics of recombination (see Fig.~\ref{fig:distortions}). 
%In summary, a detection of primordial gravitational waves consistent with the standard inflationary prediction would reveal the presence of a new fundamental energy scale for particle physics and would have far reaching implications for quantum gravity. Detecting correlations on the largest scales would confirm a primordial origin. Any departure from a nearly scale-invariant, nearly Gaussian spectrum would reveal new physics beyond the simplest inflationary model. In the absence of a detection, an improvement by about two orders of magnitude on the current upper limit would qualitatively change how we think about the inflationary paradigm.

\vspace{-0.15in}

\subsubsection{Light Relics and Dark Matter}

\vspace{-0.05in}

After inflation, the universe was reheated to temperatures of at least 10 MeV and perhaps as high as $10^{10}$ GeV.  
At these high temperatures, even very weakly interacting or very massive particles, such as those arising 
in extensions of the Standard model of particle physics, can be produced in large abundances~\cite{1979ARNPS..29..313S,Bolz:2000fu}.  As the universe expands and cools, 
the particles fall out of equilibrium and leave observable signatures in the \ac{CMB} power spectra. 
Through these effects the CMB is a sensitive probe of neutrino and of other particles' properties.  

One particularly compelling target is the effective number of light relic particle species $\Neff$, also called the effective 
number of neutrinos. The canonical value with three neutrino families is $\Neff = 3.046$. Additional light particles 
%in thermal equilibrium with the Standard model particles at any point in our history, it will 
contribute a change to $\Neff$ of $\Delta \Neff \geq 0.027\,g$ where $g \geq 1$ is the number of 
degrees of freedom of the new particle~\cite{Brust:2013xpv,Baumann:2016wac}.  
This defines a target of $\sigma(\Neff) < 0.027$ for future CMB observations. 
Either a limit or detection of $\Delta \Neff$ at this level would provide a powerful insight into the basic constituents 
of matter. 

Forecasts for $\Neff$ are shown in Figure~\ref{fig:Neff_future}.  The two most important parameters for improving constraints
are the fraction of sky observed $f_{\rm sky}$ and the noise. Achieving both larger $f_{\rm sky}$ and
lower noise are strengths of the CMB Probe compared to other platforms. 
Our baseline mission nearly reaches the target constraint with $g=1$, already exceeding constraints 
from other astrophysical probes and large regions of parameters space for lab-based searches for light particles.
\comred{dan, let's clean up the English here}
A newly designed mission is likely to reach $\sigma(\Neff) < 0.027$ with high signal-to-noise ratio. 

%Much of the information about our thermal history and the particle content of the universe is encoded in the $T$ and $E$ power spectra.  
%A high-precision measurement of these spectra over the full sky is expected to significantly improve our understanding of the post-inflationary 
%universe.  This is particularly true in $E$-mode polarization where, to date, far fewer modes have be measured at the level of cosmic variance than in temperature.

%The spectra at high-$\ell$ contain important information about the components of the thermal plasma and their interactions around the time of recombination.  
%One particular compelling target is the effective number of neutrino species $\Neff$, which parameterizes the total amount of energy density in radiation 
%at the time of recombination. Despite its common name, $\Neff$ encodes the total number of light relic particles.  The canonical value %with three species of 
%neutrinos is $\Neff = 3.046$. 
%It is defined such that in the Standard model of particle physics with normal thermal evolution, $\Neff = 3.046$ due to the energy density 
%in the three species of neutrinos.  
%$\Neff$ is also sensitive to any additional light relic particles as their gravitational influence is identical to the neutrinos.  
%In fact, if there was an 


%The presence of free-streaming radiation changes the detailed features of the $TT$, $TE$ and $EE$ spectra at all $\ell$.  
%In particular, it changes the locations of the acoustic peaks and alters the damping tail at high-$\ell$~\cite{Bashinsky:2003tk,Hou:2011ec,Follin:2015hya,Baumann:2015rya}.  Similar changes to the spectra 
%arise from many other compelling targets including the helium fraction $Y_p$ and more general dark sector physics.  For this reason, 
%constraints on $\Neff$ a useful proxy for the information available in the high-$\ell$ power spectra.  

%noise level of 0.9 $\mu$K-arcmin over the full sky gives competitive 
%constraining power when compared other proposals.  
%The full-sky nature of the proposed mission would allow for cosmic variance limited $E$-modes 
%over most of the sky and a large range of $\ell$.

%The main downside of a space-based mission is that we cannot reach the resolutions available from the ground.  
%However, we see that at 5' resolution and 1 $\mu$K-arcminute noise the forecasts are less sensitive to 
%the resolution then one might naively expected.  In particular we can reach $\sigma(\Neff) < 0.035$ for
%temperature noise from 1-2 $\mu$K-arcmin and $f_{\rm sky} =0.6-0.8$.  These forecasts are competitive 
%with CMB Stage IV.  Specifically, the larger sky fraction and sensitivity available from space appears 
%to compensate for the reduced resolution.  In fact, the full sky measurement would provide complimentary information that could be 
%combined with ground based surveys to further improve over the limits available from either experiment.  
%This is particularly important for 
%$\Neff$ which is tantalizingly close to the target of $\sigma(\Neff) =0.027$ and therefore even an apparently modest improvement 
%could have a major scientific impact.  

%Neutrino properties measurements in accelerator give a minimum value of $\sum m_\nu =58$.  
%that is accessible from Cosmology.  
%The most distinctive feature of $\sum m_\nu$ is that it suppresses the growth of structure on small scales.  This suppression
%can be measure in the CMB through amplitude of the lensing power spectra compared to the primary CMB.  In principle, 
%this relative difference can yield a measurement  of the minimum value of $\sum m_\nu =58$ meV at 4-5 $\sigma$ for a 
%number of future cosmological surveys.  However, sensitivity to $\sum m_\nu$ is ultimately limited by our knowledge of 
%the primordial amplitude of fluctuations $A_s$ which is strongly degenerate with the optical depth $\tau$. 

%The current limit on $\tau$ from the Planck satellite of $\tau = 0.055 \pm 0.009$ ultimately limits 
%$\sigma(\sum m_\nu) \gtrsim 25$ meV, as shown in the panel of Figure~\ref{fig:Neff_future}.  While the figure 
%shows the sensitivity of a space-based CMB mission to $\sum m_\nu$, this lower limit is common to any 
%measurement that depends on the relative suppression.  Therefore, a cosmological detection of 
%$\sum m_\nu = 58$~meV at 3-5 $\sigma$ depends crucially on an improvement measurement of $\tau$.  
%To date, the only proven method for such a measurement is from a space-based CMB observations.  The best 
%constraints on $\tau$ come from $E$-modes with $\ell < 20$ which requires control over the largest angular scales.  



\begin{figure}[t!]
\begin{center}
\includegraphics[width=0.45\textwidth]{figs/Neff.pdf}
\includegraphics[width=0.45\textwidth]{figs/Mnu_tauprior.pdf}
\caption{ \small \setlength{\baselineskip}{0.95\baselineskip}
$\Neff$ as a function of noise and sky fraction assuming 5' resolution (left) and
Neutrino mass constraints as a function of uncertainties in measurement of $\tau$ and noise for a 5' beam and 
sky fraction of $f_{\rm sky} = 0.7$. 
Vertical lines denote the expected performance of EPIC-IM. 
The blue dashed line is the current \planck~limit; the grey dashed line is the limit from cosmic variance 
measurement of $\tau$. All forecasts assume internal delensing of the $T$ and $E$-maps~\cite{Green:2016cjr}, including residual non-Gaussian covariances.  The $\sum m_\nu$ forecasts includes DESI BAO.  
\label{fig:Neff_future} }
\end{center}
\vspace{-0.15in}
\end{figure}

Many light relics of the early universe are not stable. They decay, 
leaving faint evidence of their past existence on other tracers. The relics with sufficiently long lifetime to survive few minutes, 
past the epoch of light element synthesis, leave a signature on the helium fraction $Y_p$.  If they decay 
by the time of recombination, their existence through this period is best measured through the ratio of $\Neff$ to $Y_p$. 
The Probe's cosmic variance limited determination 
of the $E$ power spectra will improve current limits for these quantities by roughly a factor of five thus eliminating sub-MeV mass thermal relics.   
Spectrum distortion measurements give additional constraints on the lifetime and abundance 
of such relics. Chluba et al. showed that a future Probe's $\mu$-distortion constraint gives a two orders of magnitude
improvement on the abundance and life time of early Universe relics compared to current constraints derived 
from measurements of light element abundances \comred{needs citation to the proper chluba et al, and to the constraint
from light element abundance}

%the constraints   
%derived from light element abundance by more than two orders of magnitude 

%But the existence of those with lifetime longer than few minutes 
%but shorter than 400,000 years will be detected or constrained through the CMB Probe's precise measurements 
%of the ratio of the helium fraction $Y_p$ and $\Neff$~\cite{Fischler:2010xz,Baumann:2015rya}. The values of $Y_p$
%and $\Neff$ are each sensitive to the energy content of the universe during the formation 
%of the light elements and at 400,000 years, respectively. The Probe cosmic variance limited determination 
%of the $E$ power spectra will improve current limits for these quantities by a factor of ?? thus eliminating (\comred{what? classes 
%of possible relics? what is the quantitative deliverable?} )
%can survive beyond the time of BBN
%The existence of some light relics of the early universe will be detected or ruled out by comparing the measured 
%values of helium fraction  $Y_p$ and $\Neff$. Both will be measured to an accuracy of at least ??\% by 
%Measurements of the primary CMB and CMB lensing are very sensitive to particles with long-lifetimes that survive 
%until the era of recombination.  Furthermore, the primary CMB is indirectly sensitive to BBN through the helium fraction, $Y_p$, 
%that can be detect energy injections at those times.  However, many relics of the early universe are not cosmologically stable but 
%can survive beyond the time of BBN.  Energy injection between the two eras is not directly captured by the CMB anisotropies 
%but can be tested by BBN consistency of $Y_p$ with the measured value of $\Neff$~\cite{Fischler:2010xz,Baumann:2015rya}.  

%Additional, far more sensitive measurements of this intermediate era are possible through the {\it distortions} of the 
%CMB blackbody spectrum. This will allow us to place stringent bounds on the presence of long-lived decaying 
%particles, with lifetimes $t_{\rm X}\simeq 10^6-10^{11}\,{\rm s}$ \citep{Sarkar1984, Kawasaki1986, Hu1993b, Chluba2013fore, Chluba2013PCA, Dimastrogiovanni2015}. CMB distortion measurements could thus complement existing bounds from CMB anisotropy measurements on particles with even longer lifetimes \cite{Chen2004, Zhang2007, Diamanti2014} and improving constraints derived from light-element abundances \citep{Kawasaki2005, Kawasaki2005b, Jedamzik2006} by more than two orders of magnitude, potentially breaking the degeneracy between lifetime and abundance of the particle \citep{Chluba2011therm, Chluba2013fore, Chluba2013PCA}.
%

Cosmological measurements have already confirmed the existence of one relic that lies beyond the 
Standard Model: dark matter. For a conventional WIMP candidate, the CMB places very stringent 
constraints on its properties through the signature of its annihilation on the $T$ and $E$ 
spectra\citep{Peebles2000, Chen2004, Padmanabhan2005}.  Planck currently excludes WIMPs with mass $m_{\rm dm}< 16$ GeV and a future CMB mission could reach $m_{\rm dm} < 45$ GeV for $f_{\rm sky} =0.8$.  
A dark matter candidate can also have a slow decay to Standard models particles which is 
similarly constrained by the CMB~\cite{Chen2004, Zhang2007, Diamanti2014, Slatyer:2016qyl}.  Current and future CMB limits on the lifetime of $\tau \gtrsim 10^{25}$ s are somewhat weaker than indirect detection limits of $\tau > 10^{24-28}$~s~\cite{Essig:2013goa}.  
%Through cosmological measurements, we have already confirmed the existence of one relic that lies beyond the 
%Standard Model: dark matter. Characterizing the nature of dark matter is one of the most basic problems in 
%cosmology and astro-particle physics.  For a conventional WIMP candidate, the CMB places very stringent constraints on dark matter through possible energy injection at the time of recombination.  A thermal relic will necessarily annihilate into Standard model particles which distorts the Thomson visibility function and ultimately the shape of the primary $T$ and $E$ spectra \citep{Peebles2000, Chen2004, Padmanabhan2005}.  A dark matter candidate can also have a slow decay to Standard models particles which is similarly constrained by the CMB~\cite{Chen2004, Zhang2007, Diamanti2014, Slatyer:2016qyl}.

A particle-independent approach is to constrain dark matter interactions that would 
affect the evolution of the effective dark matter fluid and its interactions with baryons or photons.  The simplest example is 
to constrain the baryon-dark matter cross section through its effective coupling of the two fluids~\cite{Dvorkin:2013cea}.  
These couplings affect the evolution of fluctuations and ultimately the $T$ and $E$ spectra. The current limits of $\sigma \gtrsim 10^{-31}-10^{-34}\,{\rm cm}^2 \times (m_{\rm dm} / {\rm MeV})$ can be competitive with direct detection for sub-GeV masses.  
More exotic dark sectors that include long-range forces can produce an even richer phenomenology in the CMB and in the large-scale structure 
without necessarily producing an associated signature in direct detection experiments or 
indirect searches (e.g.~\cite{Cyr-Racine:2013fsa,Buen-Abad:2015ova,Lesgourgues:2015wza}). 

Interactions of dark matter with standard model particles can also be constrained through 
measurements of spectral distortions\cite{Yacine2015DM}. 
%Chluba et al. showed 
%As the Universe expands, the matter cools. Compton interactions with electrons keep the normal matter at the CMB 
%temperature until well after recombination. This leads to a small distortion of the CMB with a negative chemical 
%potential~\citep{Chluba2011therm}. In a similar manner, interactions of DM with electron, protons or directly 
%with CMB photons can lead to a distortion. 
Current constraints from FIRAS are most sensitive to small dark matter
mass, $m_{\rm X}\lesssim 0.2\,{\rm MeV}$, but these could be extended to $m_{\rm X}\lesssim 1\,{\rm GeV}$ with a 
Probe-class mission, testing DM interaction down to cross-sections 
$\sigma\simeq 10^{-39}-10^{-35}\,{\rm cm}^2$~\cite{Yacine2015DM}. This complements and improves 
existing constraints~\cite{Essig2012PhRvL.109b1301E, Boehm2014MNRAS.445L..31B} \comred{by how much?}
and opens a new avenue for testing dark matter-proton interactions~\cite{Yacine2015DM}.

A host of other physical phenomena including the existence and properties of axions, primordial magnetic fields, and 
superconducting strings, leave signatures on the spectrum of the CMB and can therefore be constrained by 
the sensitive measurements  of a future Probe~\cite[e.g.,][]{Jedamzik2000, Tashiro2012, Dolgov2013, Tashiro2013, Caldwell2013}.


\vspace{-0.15in}

\subsubsection{Neutrino Mass}

\vspace{-0.05in}

One of the last unknowns of the Standard model of particle physics is the absolute mass scale of the neutrinos.  
%While measurements of neutrino oscillations demonstrate the neutrinos have mass, directly measuring the scale of the masses is challenging experimentally.  
%Current measurement of $\Neff$ confirm the existence of a cosmological abundance of neutrinos whose gravitational influence is detectable in the CMB and in large scale structure.  
Cosmology presents a unique opportunity to measure the sum of neutrino masses $\sum m_\nu$ through the 
suppression of the growth of structures in the Universe on small scales.  
%Larger $\sum m_\nu$ gives a larger suppression and the $\sum m_\nu$ can be measured by 
%The \ac{CMB} Probe would be a valuable tool in the quest for a cosmological detection of $\sum m_\nu$.   
The sensitivity to $\sum m_\nu$ from suppression of power is limited by our knowledge of 
the primordial amplitude of fluctuations $A_s$, which is strongly degenerate with the optical depth $\tau$.  
The current limit on $\tau$ from \planck\ of $\sigma({\tau}) = 0.009$~\cite{} limits 
$\sigma(\sum m_\nu) \gtrsim 25$ meV. Forcasts for an internal 
CMB measurement of $\sum m_\nu$ via CMB lensing~\cite{Kaplinghat:2003bh} are shown Figure~\ref{fig:Neff_future} but the conclusion is the same for any proposed cosmological probe.  
%This lower limit is common to any measurement that depends on the relative suppression.  
Therefore, a detection of the minimum value expected from particle physics  
$\sum m_\nu = 58$~meV at more than $2 \sigma$ depends crucially on a better measurement of $\tau$.  
The best constraints on $\tau$ come from $E$-modes with $\ell < 20$ which require 
measurements over the largest angular scales.
To date, the only proven method for such a measurement is from space.  
The \ac{CMB} Probe could reach the cosmic variance limit of $\tau \sim 0.002$ and could therefore 
reach $\sigma(\sum m_\nu) < 15$ meV when combined with DESI's measurements of 
baryon acoustic oscillations.  
A detection of $\sum m_\nu$ at this level is not possible with any other existing survey.
%if not accompanied by an improvement to the measurement of $\tau$.

\vspace{-0.15in}

\subsubsection{Cosmological structure formation}

\vspace{-0.05in}

Understanding the evolution of cosmological structures from small density perturbations through the formation of the
first stars to present day galaxies and cluster is a key goal of cosmology~\cite{dunlop2011}. 
Cosmological reionization, the transition of the Universe from dominated by neutral to ionized 
hydrogen, is a cornerstone of this evolution because it encodes information 
about the star formation history and the physical processes that formed the galaxies of various luminosities and masses we see today. 
But when did the epoch of reionization start?  How long did it last? Are early galaxies enough to reionize the entire Universe
or is another source required?
 
Measurements of the \ac{CMB} $E$ mode power spectrum over large angular scales are sensitive to the optical depth 
to reionization $\tau$, a key parameter for all reionization models that attempt to answer these questions. 
The \planck\ team  reported recently a value of $\tau=0.055 \pm 0.009$~\cite{planck2015-XLVI,planck2015-XXXI}.
The level is significantly lower than previous estimates and reduces the tension between CMB-based analyses and constraints from 
other astrophysical sources. The CMB Probe's cosmic variance limited measurement of $E$-mode polarization will 
improve the $1\sigma$ error by a factor of 4.5 and will 
set stringent constraints on models of the reionization epoch. \comred{what is the quantitative connection to models
of reionization}.

%The optical depth to reionization, $\tau$, places an important integral constraint on the extended reionization history.
%The {\it Planck} Collaboration~\cite{planck2015-XLVI,planck2015-XXXI} reported recently a value of $\tau=0.055 \pm 0.009$ significantly lower than previous estimates. 
%This suggests that an early onset of reionization is strongly disfavoured by the {\it Planck} data. 
%The {\it Planck} Collaboration~\cite{planck2015-XXXI} showed that this result reduces the tension between CMB-based analyses and constraints from 
%other astrophysical sources. 
%A cosmic variance limited measurement of E-mode polarization on large scales, possible with a probe mission, will render the most accurate 
%determination of $\tau$ (Figure~\ref{fig:Neff_future}
%shows a cosmic variance limit measurement of $\tau$ along with the current {\it Planck} limit, break the degeneracy with the neutrino mass, 
%set stringent constraints on models of the reionization epoch, and, finally, help understanding the formation of the cosmological structures we see today.

The anisotropy in the \ac{CIB} produced by dusty star-forming galaxies in a wide redshift range, are
an excellent probe of both the history of star formation and the link between
galaxies and dark matter across cosmic time. The \planck\ collaboration 
derived values of the star formation rate that,
at redshifts z$\mathrm{\sim3}$, are about three times higher
than constraints from number counts measurements (\cite{planck2014-XXX,planckXVIII,madau2014}).
The new mission probe, 
By measuring \ac{CIB} anisotropy with 100 times higher signal-to-noise ratio
the CMB Probe will shed light on this intriguing discrepancy. 
Specifically, it will constrain the star formation rate with one tenth of \planck 's uncertainty. 

\comred{need to talk to Paolo/Graca}
Moreover, it will be possible to identify and constrain a
characteristic halo mass $M_{\mathrm{eff}}$,
which determines the most efficient gas accretion and SFR, and
therefore sets the evolution of the galaxies residing within
a dark matter halo. Current models and measurements constrain this characteristic halo mass at
$M_{\mathrm{eff}}\sim 10^{12}$ solar masses with about $\mathrm{10\%}$ uncertainty, while the new 
mission probe will constrain this parameter at the percent level.

Dusty star-forming galaxies trace the underlying dark matter
field in a broad redshift range. Therefore, the anisotropy in the \ac{CIB} 
correlates with multiple dark matter tracers including catalogs of galaxies and quasars, 
and maps of the $\gamma$-ray and the X-ray background~\cite{serra2014,wang2015,cooray2016}.
Cross-correlations between the Probe's maps of the \ac{CIB} and these tracers will provide an 
additional probe of the global star formation history, and they will shed light on the interaction between 
light and matter in a broad wavelength range. \comred{the paragraph starts with dark matter, but ends 
with SFR ..?}

The transition to reionized Universe and the onset of structure formation inject
energy into the sea of CMB photons. This injection is detectable through a distinct spectral distortion. 
This is the largest expected distortion -- it is marked `$y$ Groups/Clusters' in Figure~\ref{fig:distortions} --
and will be clearly detected by the CMB Probe. 
A detection will give information about the total energy output of first stars, AGN and galaxy clusters. \comred{what do 
you do with this number? how does this feedback to constraints on SFR or other parameters of structure evolution models?}
Group-size clusters that have masses $M\simeq 10^{13}\,M_{\odot}$ contribute significantly to the signal. 
With temperature $k T_{\rm e}\simeq 1\,{\rm keV}$ these are sufficiently hot to create a relativistic 
temperature correction to the large $y$-distortion. This relativistic correction, denoted `$y$ relativistic' in 
Figure~\ref{fig:distortions},  will also be detected with high signal-to-noise ratio by the CMB Probe, and 
will be used to constrain the currently uncertain feedback mechanisms used in hydrodynamical simulations
of cosmic structure formation~\citep{Hill2015}. 

%Large-scale structure can also be probed using CMB spectral distortions measurements. 
%In fact, the largest guaranteed distortion is caused by the associated late-time energy release of 
%forming structures and from reionization~\cite{Sunyaev1972b, Hu1994pert, Oh2003, Cen1999, Refregier2000}, 
%imprinting a $y$-type distortion with $y \simeq 2\times 10^{-6}$ \citep[e.g.,][]{Refregier2000, Hill2015}. 
%This distortion is only one order of magnitude below the current limit from COBE/FIRAS and, even with most 
%pessimistic assumptions about foregrounds, should be clearly detected with the next-generation spectrometers we propose to study. 
%A detection will give information about the total energy output of first stars, AGN and galaxy clusters. \comred{what do 
%you do with this number? how does this feedback to constraints on SFR or other parameters of structure evolution models?}
%In particular, group-size clusters that have masses $M\simeq 10^{13}\,M_{\odot}$ contribute significantly to the signal. 
%With temperature $k T_{\rm e}\simeq 1\,{\rm keV}$ these are sufficiently hot to create a relativistic 
%temperature correction to the large $y$-distortion. This relativistic correction, denoted `$y$ relativistic' in 
%Figure~\ref{fig:distortions},  
%which can be used to constrain the currently uncertain feedback mechanisms used in hydrodynamical simulations
%of cosmic structure formation~\citep{Hill2015}.  (see Fig.~\ref{fig:distortions}).

The CMB spectrum varies spatially across the sky. One source of such anisotropic distortion is due to 
the spatial distribution clusters of galaxies and has already been measured by Planck~\cite{Planck2013SZ}. 
A combination of precise CMB imaging 
and spectroscopic measurements will allow observing the relativistic temperature correction of individual SZ 
clusters~\cite{Sazonov1998,Itoh98,Challinor98}, which will calibrate cluster scaling relations and inform our 
knowledge of the dynamical state of the cluster atmosphere. 

Resonant scattering of the CMB photons during and post last scattering lead to spectral-spatial signals
that can be used to constrain the presence of metals in the dark ages and the physics of 
recombination~\cite{Jose2005, Carlos2007Pol, Lewis2013,Kaustuv2004, Schleicher2008}. \comred{what is the quantitative deliverable? } 

%and post-recombination 
%eras \cite{Kaustuv2004, Schleicher2008} can lead to spectral-spatial CMB signals that can be used to constrain 
%the presence of metals in the dark ages and the physics of recombination. For all these applications, instrumental 
%synergies between CMB imaging and spectroscopy need to be studied in detail. 



%The CMB spectrum varies spatially across the sky. One source of such anisotropic distortion is related to clusters of 
%galaxies and has already been measured by Planck~\citep{Planck2013SZ}. A combination of precise CMB imaging 
%and spectroscopic measurements will allow observing the relativistic temperature correction of individual SZ 
%clusters~\citep{Sazonov1998, Itoh98, Challinor98}, which will calibrate cluster scaling relations and inform our 
%knowledge of the dynamical state of the cluster atmosphere. Finally, resonant scattering signals in the 
%recombination \citep{Jose2005, Carlos2007Pol, Lewis2013} and post-recombination 
%eras \citep{Kaustuv2004, Schleicher2008} can lead to spectral-spatial CMB signals that can be used to constrain 
%the presence of metals in the dark ages and the physics of recombination. For all these applications, instrumental 
%synergies between CMB imaging and spectroscopy need to be studied in detail. 




%\begin{figure}[htbp!]
%\hspace{0.in}
%\parbox{4.2in}{ \centerline {
%\includegraphics[width=2.0in] {figs/cmb_powspec_v1.pdf}  
%\hspace{0.1in}
%\includegraphics[width=2.0in] {Figures/nsrlabeledrp01v10s}  }  }
%\hspace{0.1in}
%\parbox{2.in}{
%\caption{ \small \setlength{\baselineskip}{0.90\baselineskip}
%    Theory and observations for the spectrum; Space of predictions from important classes of inflation models.
%\label{fig:inflation} } }   
%\vspace{-0.05in}
%\end{figure}


%A significant contamination of CMB anisotropy maps is due to
%the foreground emission from infrared (IR)
%galaxies, responsible for the cosmic infrared background (CIB).
%The CIB is the second largest
%extragalactic background after the CMB, with an approximate
%brightness of 24 nW m$\mathrm{^{-2} sr^{-1}}$ \citep{dole2006}.

%Dust enshrouded star-forming galaxies at redshift $\mathrm{z\sim 1-3}$ is heated by starlight at ultraviolet (UV) and optical wavelengths,
%and re-radiates at mid-IR to sub-millimetre wavelengths. This emission, from galaxies actively
%producing stars at their peak of star formation, reaches us in the far-infrared (FIR) regime as the cosmic infrared
%background (CIB). The CIB carries a wealth of information about the history of star formation and dark matter 
%in the Universe, and will be used to constrain foreground levels and to remove the effects of lensing 
%from the CMB polarization signals. 

%With a brightness of 24 nW m$\mathrm{^{-2} sr^{-1}}$ \citep{dole2006}, it is 
%the second most intense extragalactic background after the CMB. 
%While the CIB is not our only handle on the evolution of the
%cosmic star formation rate (SFR), it is particularly important
%because FIR/sub-millimetre surveys are not subjected to some
%uncertain steps in the conversion from galaxy counts and luminosities to SFRs,
%affecting, e.g., optical surveys.

%The drawback of working with a
%high density of faint, distant sources in the FIR regime is that
%individual objects are blended. While both the {\it Herschel} and {\it Planck} satellites
%recently performed ground-breaking measurements of the CIB
%\citep{amblard2011,viero2013a,planck2014-XXX,mak2016}, only a
%negligible fraction of {\it Planck} sources have been individually
%identified, due to its poor angular resolution, while for
%{\it Herschel} maps, only 10$\%$ of the objects
%has been resolved into individual galaxies at 857 GHz \cite{bethermin2010}.
%However, the anisotropies detected in the
%unresolved background can be analyzed through statistical tools
%such as the angular power spectrum \citep{knox2001} and, since they trace the
%underlying dark matter field, they can be interpreted with
%phenomenological models linking dark matter halos to IR galaxies,
%such as the Halo Model \cite{cooray2002,shang2012}.

%{\bf Star Formation History:}
%The Planck Collaboration, analyzing CIB anisotropy and its correlation with CMB lensing \citep{planck2014-XXX,planckXVIII},
%derived limits on the star formation rate that
%at redshift $\mathrm{z>2}$ are higher than with other datasets (see for example \cite{madau2014}) 
%\comred{by how much higher?}. With \comred{100?} times  the Planck sensitivity at \comred{??} GHz, 
%\comred{the constraints on the star formation rate will improve by ??}
% Clearly, more accurate measurements of the CIB clustering at the
% angular scales probed by {\it Planck} will be extremely useful to
%gain more insight on the evolution of the star formation rate at
% high redshift. 
%The new mission probe will measure CIB anisotropies
%with only one tenth of {\it Planck}'s instrumental noise at the critical
%scales where the clustering of galaxies in the same dark matter
%halo (the 1-halo term) has the same amplitude as the
%clustering due to galaxies in separated halos
%(the 2-halo term). Assuming a precise knowledge of the Poisson level of CIB
%galaxies, we will be able to firmly constrain our models of CIB clustering,
%and thus address three of the seven key questions
%identified in the Astro2010 report ``New Worlds, New Horizons in Astronomy and Astrophysics''
%(NAS Decadal Survey, p. 47): {\it What is the fossil record of galaxy assembly                                                   
%from the first stars to present? What are the connections                                           
%between dark and luminous matter? How do cosmic structures form and evolve?}
%\comred{deliverables from previous paragraph not clear} 

%{\bf Dark Matter:}
%The CIB, being a tracer of the dark matter field over a broad redshift range,
%can be cross-correlatated with many other datasets to explore
%the interplay between CIB galaxies and dark matter. examples include the cross-correlations
%with catalogs of quasars \citep{wang2015} and
%galaxies \citep{serra2014} to constrain the interplay between
%SFR and halo mass, and the cross-correlation with the Cosmic
%$\mathrm{\gamma}$-ray background from {\it Fermi}-LAT
%\citep{fermi2016} to constrain the dark matter annihilation
%cross-section \citep{cooray2016}.
%\comred{what are the quantitative outcomes of these cross-correlations}
%Beyond the
%cross-correlation with the lensing of the CMB
%\citep{planckXVIII,holder2013}, some other 

%{\bf CMB Delensing:} Since they are both tracers of the underlying mass distribution over
%a broad range of redshifts, the CIB and CMB lensing are highly correlated
%\citep{planckXVIII}. In particular, the CIB can be used as
%an ideal proxy for the CMB lensing field in delensing studies, aiming at
%reducing the confusion due to B-modes from lensing in the search of the
%signal from primordial gravitational waves.
%Recently \cite{sherwin2015,larsen2016} showed that co-adding {\it Planck} CIB maps
%greatly improves the delensing performance. Upcoming CMB surveys
%will heavily rely on delensing methods for constraining the
%inflationary B-mode polarization signal, and CIB delensing of temperature and E-mode
%polarization might also help improving constraints on other parameters such as the effective
%number of neutrino species $\mathrm{N_{eff}}$ \citep{larsen2016}.
%\comred{can we be quantitative}

%{\bf CMB Foregrounds:} The Planck collaboration found that the CIB is 
%a significant contributor to foregrounds in the 143x217 and 217x217 GHz 
%band correlations~\citep{planck2016like}. Both the clustering and Poisson components of the 
%CIB were found to be important. The cross-correlation between IR galaxies and the thermal
%Sunyaev-Zeldovich (tSZ) effect provides an additional contamination. 
%Thus, an accurate determination of both CIB and CIB-tSZ power
%spectra will be extremely useful when accounting for these foregrounds
%in the CMB parameter estimation.
%\comred{make quantitative?} 

%However, constraining the history of star formation is not the only reason for measuring CIB anisotropies with increased sensitivity from very large to very small scales. Below, we briefly discuss some others. 
%\begin{itemize}
%\item The CIB is an important foreground for CMB studies. As shown in \cite{planck2016like}, a significant contribution to the astrophysical foreground in the 143x217 and 217x217 GHz channels is due to both the clustering and Poisson components of the CIB. The cross-correlation between IR galaxies and the thermal Sunyaev-Zeldovich (tSZ) effect provides an additional contamination. Thus, an accurate determination of both CIB and CIB-tSZ power spectra will be extremely useful when accounting for these foregrounds in the CMB parameter estimation.
%\item The CIB, being a tracer of the dark matter field over a broad redshift range, can be cross-correlatated with many other datasets to explore the interplay between CIB galaxies and dark matter. Beyond the cross-correlation with the lensing of the CMB \citep{planckXVIII,holder2013}, some other examples include the cross-correlations with catalogs of quasars \citep{wang2015} and galaxies \citep{serra2014} to constrain the interplay between SFR and halo mass, and the cross-correlation with the Cosmic $\mathrm{\gamma}$-ray background from {\it Fermi}-LAT \citep{fermi2016} to constrain the dark matter annihilation cross-section \citep{cooray2016}.
%\item Since they are both tracers of the underlying mass distribution over
%a broad range of redshifts, the CIB and CMB lensing are highly correlated
%\citep{planckXVIII}. In particular, the CIB can be used as
%an ideal proxy for the CMB lensing field in delensing studies, aiming at
%reducing the confusion due to B-modes from lensing in the search of the
%signal from primordial gravitational waves.
%Recently \cite{sherwin2015,larsen2016} showed that co-adding {\it Planck} CIB maps
%greatly improves the delensing performance. Upcoming CMB surveys
%will heavily rely on delensing methods for constraining the
%inflationary B-mode polarization signal, and CIB delensing of temperature and E-mode
%polarization might also help improving constraints on other parameters such as the effective
%number of neutrino species $\mathrm{N_{eff}}$ \citep{larsen2016}.
%\end{itemize}
%To summarize, the CIB is a full sky, bright, high redshift extragalactic
%background that maps star formation at its peak, and carries
%a tremendous amount of information about the birth and
%evolution large scale structures in the Universe, and the interplay
%between light and matter.


% 
%
% Some of the most important information is on the largest scales: super-horizon correlations
% What do we learn: new energy scale for fundamental phenomena in particle physics; energy scale of inflation/Hubble parameter during inflation; field range and q. grav; classes of inflationary potentials; with a detection, can go after shape of the spectrum, NG. These constrain non-minimal inflation models (secondary sources), spectrum of physics BSM through cosmic strings; Any alternatives to inflation or to Einstein gravity (massive gravity, etc) must be consistent with the measured spectrum.  
% any additional power for scalar sector?
 
 %***********************  The placeholder text is below ***************************%
%\comred{The verbiage below is taken from another proposal. Here we need to explain what are the science objectives 
%of the CMBProbe, how the science objectives relate to the current state of knowledge, and to NASA's goals}
%
%
%The paradigm of inflation~\cite{guth81,linde82,albrecht82,sato81,kolb94}
%%, in which the Universe underwent exponential expansion within the first $\sim$$10^{-35}$~sec, 
%makes several predictions that are consistent with all current astrophysical 
%measurements~\cite{spergel06,Tegmark:2006az,planck2015parameters,planck2015inflation}. 
%A robust prediction of inflation is the existence of a stochastic background of gravitational radiation 
%with an amplitude depending on the mechanism driving the accelerated 
%expansion~\cite{starobinsky82,starobinsky83a,rubakov82,grishchuk75,abbott84a}.
%In most scenarios, this `inflationary gravitional wave background' (\igb) is predicted
%to have a spatial power spectrum whose amplitude is proportional to the energy
%scale of inflation $V^{1/4}$ via
%$V^{1/4} = 3.7 \times 10^{16} \ r^{1/4}\,\, {\rm GeV},$
%where $V$ is the inflaton potential and $r$ is the ratio of the temperature
%quadrupoles produced by gravitional waves and by density perturbations.  
%There are theoretical reasons $V^{1/4}$ may be close to the Grand
%Unification scale of $10^{16}$~GeV, suggesting detectable $r$ values between 
%$\sim$0.001 and $\sim$0.1. In addition to determining the energy scale of inflation, measurements 
%of the \igb\ probe the scalar field potential at or above the Planck scale, which is particularly relevant for inflation models motivated 
%by string theory~\cite{SnowmassInflationTheory}. Measurements of the \igb\ thus probe fundamental physics at the 
%highest possible energy scales. 
%\begin{figure}[htbp!]
%\hspace{0.in}
%\parbox{4.2in}{ \centerline {
%\includegraphics[width=2.0in] {Figures/sunny_skies.jpg}  
%\hspace{0.1in}
%\includegraphics[width=2.0in] {Figures/sunny_skies2.jpg}  }  }
%\hspace{0.1in}
%\parbox{2.in}{
%\caption{ \small \setlength{\baselineskip}{0.90\baselineskip}
%       Sample Figure of Sunny Skies
%\label{fig:sunny_skies} } }   
%\vspace{-0.05in}
%\end{figure}
%
%The most promising way to search for the \igb\ is through its signature on the CMB polarization~\cite{kamionkowski97b,seljak97}.  
%Primordial energy density perturbations produce only a curl-free, or `E-mode', pattern of polarization.
%Gravitional waves also produce a curl, or `B-mode', pattern of polarization that density perturbations cannot
%produce~\cite{kamionkowski97a,zaldarriaga97}.  The amplitude of the B mode is related to the energy scale
%of inflation by $V^{1/4}=2\times10^{16} \ ( B_{peak} / 0.1\,\mu{\rm
%K})^{1/2} \,{\rm GeV},$ where $B_{peak}$ is the amplitude of the power spectrum of the B mode in \microk\ at $\ell=80$;
%see Fig.~\ref{fig:sunny_skies}. In its recent report New Worlds New Horizons (NWNH), the decadal survey 
%committee strongly endorsed sub-orbital searches for the B-mode signal from 
%inflation saying that ``The convincing detection of B-mode polarization in the CMB produced in the 
%epoch of reionization would represent a watershed discovery.''~\cite{blandford2010}
%
%B-mode signatures near the expected \igb\ peak at $\ell=80$ have recently been detected by BICEP2~\cite{bicep2Bmode}. 
%However, the combination of Planck data with those from the BICEP2 and Keck Array collaborations have demonstrated 
%that the B-mode signal measured is entirely consistent with contributions from polarized emission of Galactic dust and the 
%signal from the gravitational lensing of CMB photons by the large scale structure of the Universe (see 
%Section~\ref{sec:lensing})~\cite{bkp2015,planck2014-XXX,2016PhRvL.116c1302B}. 
%These data give an upper limit of $r<0.09$ at 95\% confidence level.
%Most importantly, the constraint is largely limited by Planck's noisy measurement of the dust properties in the 353~GHz band; 
%a noiseless dust map could shrink the constraint by a factor of two~\cite{bkp2015}. 
%Further progress --- detections or improved limits --- requires instruments 
%with higher sensitivity at {\it both} the dust and CMB frequency bands so that this Galactic foreground can be properly identified 
%and removed. 
%
%