science_objectives.tex

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

\vspace{-0.05in}

The broad array of fundamental questions the CMB Probe will address, as describe in this section, 
firmly fit into NASA's strategic plan as articulated by its Strategic Goal~1 ``Expand the frontiers of knowledge", and 
specifically Objective~1.6 ``Discover how the universe works, [and] explore how it began and evolved".

\vspace{-0.22in}
 
\subsubsection{The Primordial Universe and Cosmic Inflation}

\vspace{-0.05in}

%The observed temperature and $E$-mode polarization of the \ac{CMB} imply the existence of primordial 
%density perturbations that were generated long before recombination, providing a remarkable 
%observational link to the dynamics of the universe near the big bang.
%In the context of general relativity, these primordial density perturbations can be generated causally 
%either during a contracting phase followed by a bounce or during inflation, a primordial era of 
%accelerated expansion.
%Inflation, a primordial era of accelerated expansion, provides a compelling dynamical origin for the observed nearly scale-invariant spectrum of these primordial perturbations~\cite{guth81,linde82,albrecht82,sato81,kolb94}. 
%Unlike observationally viable bouncing cosmologies, 
The simplest models of inflation, a primordial era of accelerated expansion, predict an as yet 
unobserved primordial gravitational waves with a nearly scale-invariant spectrum, sourced by 
quantum fluctuations of the tensor component of the metric. 
%In addition to primordial density perturbations inflation 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 leave a distinct $B$-mode imprint on the polarization of the \ac{CMB}. Any 
detection of primordial $B$-mode polarization, whether generated by the gravitational waves 
of inflation~\cite{kamionkowski97a,zaldarriaga97} or any other source of vector or tensor perturbations, 
such as primordial magnetic fields \cite{Seshadri:2000ky,Lewis:2004ef,Ade:2015cao,Zucca:2016iur} and 
cosmic strings \cite{Turok:1997gj,Seljak:2006hi,Avgoustidis:2011ax,Moss:2014cra} would reveal completely 
new information about the early universe. The results would either provide additional confirmation for 
current models or could overturn them. A detection would also have implications for fundamental physics 
by providing evidence for a new energy scale near the GUT scale, probing physics well beyond that reachable
with terrestrial colliders. 
\begin{figure}[t]
\vspace{-0.15in}
\begin{center}
\includegraphics[width=3in]{figs/cmb_powspec_v1.pdf}  
\includegraphics[width=3in]{figs/cmbbb_powspec_v1.pdf}
\end{center}
\vspace{-0.3in}
\caption{ \small \setlength{\baselineskip}{0.95\baselineskip}
Predicted determination of the \ac{CMB} power spectra for EPIC-IM (grey boxes) after foreground removal for $r=0$ (left) and after foreground removal and delensing for $r=0.001$ (right) overlaid on theoretical predictions (solid lines) and including \planck\ measurements of the temperature and $E$ modes (dark blue) and of several ground-based measurements of the lensing $B$ modes.  The primordial $B$ mode predictions (blue) are shown for two values of $r$. 
\label{fig:clall} }
\vspace{-0.05in}
\end{figure}

%For example, in single-field inflation 
%the potential energy density $V$ of the inflaton is related to the tensor-to-scalar ratio $r$ by 
%$V^{1/4} = 3.3 \times 10^{16} \ r^{1/4}\,\, {\rm GeV}$. 

%Figure~\ref{fig:clall} shows current CMB data, $B$ modes from vacuum fluctuations of the metric during an inflationary era for two representative values of $r$, as well as forecasts for the determination of the \ac{CMB} spectra for EPIC-IM. 
To test inflation, the largest scales $\ell \leq 10$ are particularly important because they may reveal 
the presence of $B$-mode correlations on scales that were super-horizon at the time of 
recombination~\cite{Lee:2014cya}, 
and because on large scales the signal is strongest relative to the lensing $B$ mode and instrumental 
noise; see Figure~\ref{fig:clall}.
%In its recent report New Worlds New Horizons (NWNH), the decadal survey committee strongly endorsed 
%searches for $B$ modes from inflation saying, ``The convincing detection of $B$-mode polarization in 
%the CMB produced in the epoch of reionization would represent a watershed discovery.''~\cite{blandford2010}. 
% Figure~\ref{fig:clall} shows current CMB data, $B$ modes from vacuum fluctuations of the metric 
%during an inflationary era 
%for two representative values of $r$, forecasts for the determination 
%of the \ac{CMB} spectra for EPIC-IM as well as the lensing residual and noise.
No sub-orbital platform has yet produced measurements of $B$ modes at $\ell< 40$, and a satellite is by 
far the most suitable platform for the all-sky observations necessary to reach the lowest modes, $\ell<20$. 

%\vspace{-0.1in}

In slow-roll inflation there are two classes of models that naturally explain the measured value of the spectral index 
of primordial fluctuations $n_{\rm s}$. 
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; see Figure~\ref{fig:nsrp001}. 
%The most recent constraint on the tensor-to-scalar ratio is $r < 0.07 \, (95\%)$; see Figure~\ref{fig:nsrp001}~\cite{Array:2015xqh}. 
\begin{figure}[ht!]
\hspace{-0.1in}
\parbox{4.in}{\centerline {
\includegraphics[width=4.2in]{figs/nsrlabeledrp001v2} } }
\hspace{-0.05in}
%\end{center}
\parbox{2.5in}{
\caption{ \small \setlength{\baselineskip}{0.90\baselineskip}
Current $1$ and $2\sigma $ limits on $r$ and $n_{\rm s}$ (blue)~\cite{Array:2015xqh} and forecasted constraints for a fiducial 
model with $r=0.001$ for the baseline probe. 
Also shown are predictions for the models of the inflaton potential discussed in the text.
\label{fig:nsrp001} } }
%\vspace{-0.1in}
\end{figure}

Another class of models includes $R^{2}$ 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 virtually all models that naturally explain $n_{\rm s}$. 
The baseline probe would achieve $\sigma(r)\sim1.3 \times 10^{-4}$ assuming $r=0.001$. (This
prediction includes subtraction of a Galactic dust foreground model with two component power law emissivities, 
synchrotron emission with a single power law, that all power laws are spatially uniform, and self delensing.) 
%Such a model is highly optimistic and including a simple model of spatially varying frequency dependence degrades the limits by $\sim 2$.  

%A detection of $B$ modes consistent with a primordial spectrum of vacuum fluctuations would be the first observation 
%of a phenomenon directly related to quantum gravity. 
A detection of $B$ modes consistent with a primordial spectrum of vacuum fluctuations would be the first observation of a phenomenon directly related to quantum gravity. In addition, a Probe mission would allow a high significance detection of any model of large-field inflation.
%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 $\Delta\phi \gtrsim M_{\rm P}$. Studies of inflation in the context of quantum gravity give a generic 
%expectation $\Delta\phi \lesssim M_{\rm P}$~\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 
motivation to better understand how large-field inflation can be naturally incorporated into quantum gravity~\cite{Banks:2003sx,Baumann:2014nda,Brown:2015iha,Rudelius:2015xta,Silverstein:2008sg,Kaloper:2008fb,Marchesano:2014mla,Blumenhagen:2015xpa}. 

Inflation predicts a $B$-mode spectrum with the shape shown in Figure \ref{fig:clall}, but there may be 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 a Gaussian and nearly scale-invariant spectrum for 
gravitational waves. A target constraint of $\sigma(n_{\rm t})<1$ at $r=0.01$, easily achievable with a Probe mission, would significantly constrain non-vacuum 
inflationary sources~\cite{Namba:2015gja,Peloso:2016gqs}.
% and rule out physics completely inconsistent with inflation. 

Deeper mapping of large scale $E$ modes will provide new tests of isotropy, a prediction of most models of inflation; 
for example, observations with a CMB Probe could reject at 99\% confidence models designed to explain the alignment of low 
multipoles in the temperature maps~\cite{Dvorkin:2007jp}. 
Cosmic variance limited measurement of these modes will also improve constraints on $n_{s}$, 
its changes with scale, and on primordial non-Gaussianity 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}{0.90\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 baseline spectrometer 
(Probe, dash) gives approximately 10 times the Explorer mission's 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 Figure~\ref{fig:distortions}~\cite{Chluba2012, Chluba2016LCDM}. 
A Probe may also give the sensitivity to detect the signature of recombination 
radiation imprinted by recombination of hydrogen and helium 
at redshift $z\simeq 10^3-10^4$; see Figure~\ref{fig:distortions}~\citep{Sunyaev2009, Chluba2016}. 
The detailed physics is sensitive to the values of $n_{\rm s}$, which is a direct probe of inflation. 


%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{-0.18in}

\subsubsection{Light Relics and Dark Matter}

\vspace{-0.05in}

In the inflationary paradigm, the universe was reheated to temperatures of at least 10 MeV and perhaps as high as $10^{12}$ 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, leaving 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 powerful insights 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 $g=1$. 
A newly designed mission with only 10 times higher sensitivity will reach $\sigma(\Neff) < 0.025$.  A high precision measurement of the 
CMB in temperature and polarization is the only proven approach to reach this important threshold.  

\begin{figure}[t!]
\begin{center}
\includegraphics[width=0.45\textwidth]{figs/Neff_log.pdf}
\includegraphics[width=0.45\textwidth]{figs/Mnu_tauprior_log.pdf}
\vspace{-0.15in}
\caption{ \small \setlength{\baselineskip}{0.95\baselineskip}
$\Neff$ uncertainty as a function of noise and sky fraction (left) and sum of 
neutrino masses uncertainty as a function of noise and the uncertainty in the measurement of $\tau$, 
for 0.7 sky fraction (right). The resolution assumed is 5'.  
Vertical lines denote the expected performance of the baseline mission. 
The upper blue dashed line is the current \planck~limit; the lower grey dashed line is the limit from cosmic variance 
limited 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 include 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 $E$-mode power spectra will improve current limits for these quantities by
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 \citep{Sarkar1984, Kawasaki1986, Hu1993b, Chluba2011therm}. 
The Probe's $\mu$-distortion measurement gives a two orders of magnitude improvement on the 
abundance and lifetime of early universe relics compared 
to current constraints derived from measurements of light element 
abundances~\cite{Chluba2013fore, Chluba2013PCA,Kawasaki2005, Jedamzik2006}.

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 $f_{\rm sky} =0.8$.  The 
CMB provides the most stringent constraints on the dark matter annihilation cross section for dark matter 
in this mass range.  
%The CMB is complimentary to direct detection experiments which probe the scattering 
%cross-section of dark matter with standard model particles.

%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}.  

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 $\sigma \lesssim 10^{-31}-10^{-34}\,{\rm cm}^2 \times (m_{\rm dm} / {\rm MeV})$ 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's spectrum measurement 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, thus testing DM interaction down to cross-sections 
$\sigma\simeq 10^{-39}-10^{-35}\,{\rm cm}^2$~\cite{Yacine2015DM}. 
%This provides new constraints on the low mass end, $m_{\rm X}\lesssim 10\,{\rm MeV}$ and improves existing limits~\cite{Essig2012PhRvL.109b1301E, Boehm2014MNRAS.445L..31B} by up to a factor of $\simeq 50$. 
Spectral distortion measurements also open 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{-0.18in}

\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 is uniquely capable of measuring the sum of neutrino masses, $\sum m_\nu$, through the 
suppression of the growth of structures in the universe on small scales.   However, all cosmological 
measurements of $\sum m_\nu$ are fundamentally limited by our uncertainty in $\tau$ due to the strong degeneracy 
between the optical depth to reionization $\tau$ and the amplitude of the primordial perturbation power spectrum
$A_s$.  Although many surveys hope to detect $\sum m_\nu$, any detection 
of the minimum value expected from particle physics $\sum m_\nu = 58$~meV at more than $2 \sigma$ will 
require 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 current limit of $\sigma({\tau}) = 0.009$ is from \planck~\cite{planck2016_xlvi}.  Forecasts for a
CMB measurement of $\sum m_\nu$ using lensing $B$ modes~\cite{Kaplinghat:2003bh} are shown in 
Figure~\ref{fig:Neff_future}.  With the current uncertainty in $\tau$ one is limited to  
$\sigma(\sum m_\nu) \gtrsim 25$ meV; no other survey or cosmological probe would improve this constraint.  
But the \ac{CMB} Probe will reach the cosmic variance limit of $\tau \sim 0.002$ and will therefore 
reach $\sigma(\sum m_\nu) < 15$ meV when combined with DESI's measurements of 
baryon acoustic oscillations~\cite{Levi:2013gra}.  Robustly detecting neutrino mass at  $> 3\sigma$ in any cosmological setting is 
only possible with an improved measurement of $\tau$ like the one achievable with the \ac{CMB} Probe.

%A detection of $\sum m_\nu$ at this level is not possible with any other existing survey.

%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{planck2016_xlvi} limits 
%$\sigma(\sum m_\nu) \gtrsim 25$ meV. Forecasts 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 cosmological detection of the minimum value expected from particle physics  
%$\sum m_\nu = 58$~meV at more than $2 \sigma$ will require a better measurement of $\tau$.  

%The \ac{CMB} Probe will reach the cosmic variance limit of $\tau \sim 0.002$ and will therefore 
%reach $\sigma(\sum m_\nu) < 15$ meV when combined with DESI's measurements of 
%baryon acoustic oscillations~\cite{Levi:2013gra}.  
%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{-0.18in}

\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 clusters is a key goal of cosmology. An open frontier in this quest is  
to discover the details of reionization -- the transition of the universe from dominated by neutral to ionized 
hydrogen -- and to establish a connection between the history of reionization and our knowledge of galaxy evolution. 
When did the epoch of reionization start?  How long did it last? Are early galaxies enough to reionize the entire 
universe or is another population required?

%In particular, understanding cosmological reionization, the transformation of neutral hydrogen into an ionized state on a global scale, and establishing a connection between the history of reionization, its sources and our knowledge of galaxy is an open frontier.  

%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 star formation history and the physical processes that formed galaxies of various luminosities and masses. 
%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. 
The \planck\ team  reported recently a value of $\tau=0.055 \pm 0.009$~\cite{planck2016_xlvi,planck2016_xxxi}.
The level is lower than previous estimates and reduces the tension between CMB-based analyses and constraints from 
other astrophysical sources~\cite{Robertson:2015uda}.  
%While the average redshift at which reionization occurs is found to be $z_re\simeq 8$ assuming an 
%instantaneous reionization, suggesting that reionization occurred rather late.
The CMB Probe's measurement of $E$-mode polarization will 
improve $\sigma(\tau)$ by a factor of 4.5, reaching the cosmic 
variance limit and setting stringent constraints on models of the reionization epoch. 
% that require additional sources of reionization, non-standard early galaxies, 
%or significantly evolving escape fractions or clumping factors. On the whole a better estimate of $\tau$ when combined with direct probes at low redshift, 
%will help to characterize the duration of the epoch of reionization and tell us when it started.

%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 of the \ac{CIB}, produced by dusty star-forming galaxies in a wide redshift range, is
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 up to redshifts z$\mathrm{\sim 4}$~\cite{planck2014-XXX,planckXVIII,madau2014}). 
By measuring \ac{CIB} anisotropy with $\simeq$ 100 times higher signal-to-noise ratio at multiple frequencies, the CMB Probe 
will constrain the star formation rate with one tenth of \planck 's uncertainty.  Similar improvement 
will be achieved in constraining $M_{\mathrm{eff}}$, the galaxy halo mass that is most efficient in producing star 
formation activity.
%For example, a key parameter in 
%simulations of the angular power spectrum of the \ac{CIB} 
%is $M_{\mathrm{eff}}$, the galaxy halo mass that is most efficient in producing star 
%formation activity. Comparing measurements of the power spectrum to simulations
%constrains this parameter, which informs structure formation models. Current models and measurements 
%find $M_{\mathrm{eff}}\sim 10^{12}$ solar masses with about $\mathrm{10\%}$ uncertainty. 
%The CMB 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, a wealth of information will be extracted by 
%correlating the anisotropy in the \ac{CIB} 
%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}.
%These cross-correlations will provide an additional probe of the 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 ..?}

Reionization of the 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 -- marked `$y$ Groups/Clusters' in Figure~\ref{fig:distortions} --
and will be clearly detected by the Probe. 
A detection will give information about the total energy output of the first stars, AGNs, and galaxy clusters, 
an important parameter in structure formation 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 Probe. It
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 of clusters 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 leads to spectral-spatial signals
that can be used to constrain the abundance of metals in the dark ages and therefore the make-up of the 
first, and subsequent generations of stars~\cite{Jose2005, Carlos2007Pol, Lewis2013,Kaustuv2004, Schleicher2008}. 

\vspace{-0.18in}

\subsubsection{Galactic Magnetic Fields and The Star Formation Process}

\vspace{-0.05in}

Magnetohydrodynamic turbulence is a key regulator of the star-formation process. It acts over a range of spatial scales extending 
from the the largest eddies in the diffuse interstellar medium down to the scales of protostellar cores, envelopes, disks, outflows, and jets.  
Despite extensive work on observing density, velocity, and magnetic field structure, key questions remain open.  For example, 
we don't yet know the characteristic magnetic field strength in molecular clouds, nor do we know the scales and mechanisms for 
dissipation of magnetized turbulence.  Recent years have witnessed the development of sophisticated high-resolution 
3-d simulations of magnetized turbulence, allowing us to constrain both the field structure and the associated grain alignment 
parameters via statistical comparisons between observed and simulated submillimeter-wave polarization maps.  
%Early work along these lines employs both balloon-borne and ESA/Planck observations (Fissel et al. 2016; Planck collaboration 2015x).  
Our proposed probe-scale mission will provide tens of millions of independent magnetic field measurements, 
covering the missing spatial scales not recoverable via interferometric polarimetry with the Atacama Large 
Millimeter-Submillimeter Array, and thereby characterizing definitively the magnetic links between protostellar structures and the Galactic ISM.