Cosmology with the Cosmic Microwave Background
Tarun Souradeep
Inter-University Centre for Astronomy and Astrophysics,
Post Bag 4, Ganeshkhind, Pune 411 007, India.
email: [email protected]
homepage: http://www.iucaa.ernet.in/∼tarun/
The ‘standard’ model of cosmology must not only explain the dynamics of homogeneous background
universe, but also satisfactorily describe the perturbed universe – the generation, evolution and finally, the
formation of large scale structures in the universe. It is fair to say much of the recent progress in cosmology
has come from the interplay between refinement of the theories of structure formation and the improvement
of the observations [1]. Cosmic microwave background (CMB) has been by far the most influential cosmological observation driving advances in current cosmology. CMB research is well recognized as a prime
thrust area of Astronomy and Astrophysics in the science community world-wide. The Cosmic microwave
background (CMB), a nearly uniform, thermal black-body distribution of photons throughout space, at a
temperature of 2.7 degrees Kelvin, accounts for almost the entire radiation energy density in the universe.
The CMB comprises of the oldest photons that last interacted when the universe was only 0.3 million years
old (compared to the present age of 14 billion years). The photons have freely traveled right from the edge
of the observable universe a distance of about 43 billion light years (14 Giga-parsecs) as explained using
Figure 1.
The Nobel prize in Physics in 2006 has been awarded to John Mather (NASA Goddard flight center,
USA) and George Smoot (University of Berkeley, USA), who led experimental teams of the pioneering
Cosmic Background Explorer (COBE) mission - a US space Administration, NASA, satellite launched in
1989 to measure the Cosmic microwave background radiation with unprecedented accuracy over the full sky.
The COBE mission led by John Mather was a gigantic collaboration of over 1000 scientists and engineers.
The satellite operated for 4 years in a circumpolar orbit at an altitude of 900 km. COBE carried three different
instruments: FIRAS (Far infrared Absolute spectrophotometer), DMR (Differential microwave radiometer)
and DIRBE (Diffuse Infrared Background experiment). John Mather was the Principle Investigator (PI) of
the FIRAS experiment that measured the energy distribution of CMB photons to unprecedented accuracy.
George Smoot was the PI of the DMR instrument that measured, for the first time, the small variations of the
CMB temperature on the sky. The exquisite measurement of the energy spectrum by COBE- FIRAS and,
the first detection of the subtle variations in the temperature of the CMB sky by COBE-DMR, heralded a
golden era of cosmology.
The theoretical prediction of a nearly perfect black-body CMB dates to the early nucleosynthesis calculations of Gamow and collaborators within the Hot big-bang model. The serendipitous discovery of this extra
galactic microwave background by Penzias and Wilson in 1965 provided a big boost to the hot Big-Bang
model that also won the Nobel prize in Physics in 1978. It was followed up by numerous measurements of
the CMB flux at other wavelengths that were broadly consistent with a black-body spectrum. The COBEFIRAS instrument measured radiation flux in the 60-2880 GHzfrequency band. The flux measurement at
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Figure 1: A cartoon explaining the Cosmic Microwave Background (CMB) using a space-(conformal) time
diagram The present universe is transparent and CMB photons travel to us freely over cosmic distances along
our past light cone. In an expanding universe, the temperature of the Planck Black-body CMB is inversely
proportional to the expansion factor. When the universe is about 1100 times smaller, the CMB photons
are hot enough to keep the baryonic matter in the universe (about 3 quarters Hydrogen, 1 quarter Helium)
ionized, accompanied by a sharp transition to an opaque universe. The CMB photons unimpeded come to
us directly from this Spherical opaque surface of last scattering at distance of R H = 14 Gpc that surrounds
us – a super IMAX cosmic screen. The red circle depicts the sphere of last scattering in the reduced 2 + 1
dimensional representation of the universe.
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Figure 2: The figure shows a selected compilation of the best measurements of the energy spectrum of the
CMB photons as a function of frequency. The distribution is extremely well fit by a black-body spectrum at
a temperature of T0 = 2.726(±0.002) making the CMB the most perfect Black-body known in nature. The
blue measurement points around the peak (from 60-600 GHz.) are from the FIRAS instrument on board the
COBE satellite that won the Nobel prize in Physics in 2006. The figure has been obtained from the website
of the ARCADE experiment that has recently made accurate measurements of the temperature at a lower
frequency of 10 GHz.
a given frequency can be converted into an equivalent thermodynamic temperature for the CMB. FIRAS
established that the energy spectrum of CMB photons in the frequency range of 60-600 GHz is accurately
described by a perfect black-body distribution at a precisely determined temperature of T 0 = 2.726 ± 0.002
Kelvin. Possible deviations from a perfect black-body spectrum have to be smaller than a hundredth of
a percent of the peak brightness. This result alone ruled out alternate, non-cosmic (local astrophysical)
interpretations of microwave background, and established CMB as the relic of Big Bang – poetically, the
‘afterglow of cosmic creation’.
The CMB photons arriving from different directions in the sky show tiny variations in temperature, at
a level of ten parts per million, i.e., tens of micro-Kelvin, referred to as the CMB anisotropy, and a net
linear polarization pattern at micro-Kelvin to tens of nano-Kelvin level. The tiny variation of temperature
and linear polarization of these black-body photons of the cosmic microwave background arriving from
different directions in the sky faithfully encodes information about the early universe and have traveled
unimpeded across observable universe making them excellent probe of the universe. The Cosmic microwave
background radiation sky is essentially a giant, cosmic ‘super’ IMAX theater screen surrounding us at a
distance of 14 Gpc with a snapshot of the universe at a time very close to its origin. This is illustrated in the
cartoon in Figure 1.
It is convenient to express the sky map
the CMB temperature anisotropy in the direction n̂ as a
P∞of P
spherical harmonic expansion : ∆T (n̂) = `=2 `m=−` a`m Y`m (n̂) . Theory predicts that the primary CMB
anisotropy is a zero mean Gaussian field that is statistically orientation independent (statistical isotropy).
Current observations remain fully consistent with this expectation. The anisotropy can then be characterized
solely in terms an angular spectrum C` = h|a`m |2 i, where the angular brackets imply ensemble average.
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The C` spectra for wide variety of models share a generic set of features neatly related to basics physics
of primary CMB anisotropy. The anisotropy in the cosmic afterglow carries a well preserved and easily
decipherable record of the tiny seed perturbations that eventually gave rise to every bit of the grand structures
observed in the universe - the galaxies, clusters and super-clusters of galaxies. On the large angular scales
(low multipole l), the CMB anisotropy directly probes the primordial power spectrum on scales enormously
larger than the ‘causal horizon’. On smaller angular scales, the CMB temperature fluctuations probe the
physics of the coupled baryon-photon fluid through the imprint of the acoustic oscillations in the ionized
plasma sourced by the same primordial fluctuations. The physics of CMB anisotropy is well understood, the
predictions of the linear primary anisotropy and their connection to observables are unambiguous [2].
The transition to precision cosmology has been spearheaded by the measurements of CMB anisotropy
and, more recently, polarization. The COBE-DMR detection of CMB anisotropy observationally established
the origin and mechanism of structure formation in the universe. Observations were made at three frequencies, 90, 53 and 31 GHz which allowed a fairly good removal of the ‘foreground’ contamination of the
cosmic signal by the strong emission from our own galaxy. The 15 years old experimental success story
CMB anisotropy measurements, starting from discovery of CMB anisotropy by the COBE satellite in 1992
has been topped off by the exquisite data from the Wilkinson Microwave Anisotropy Probe (WMAP) of
NASA first released in 2003 and again in 2006. The WMAP space mission was launched in July 2001. The
satellite is placed at the second Lagrange point of the Sun-Earth system. Measurements from the Wilkinson
Microwave Anisotropy Probe combine high angular resolution with full sky coverage and high sensitivity
due to the stable thermal environment allowed by a space mission. Similar to the observational strategy of
COBE-DMR, the satellite measures CMB temperature differences between a pair of points in the sky. Each
day the satellite covers 30% of the sky, but covers the full sky in 6 months. This massive redundancy in measurements allows the mission to beat down the detector noise to from milli-Kelvins to tens of micro-Kelvin
level. The WMAP mission plans to continue to acquire data for eight years and make that public at regular
intervals after a short proprietary possession.
The public availability of these remarkable data sets have prompted intense activity in research groups
worldwide and has ushered in a new scientific sociology of global participation. A collaboration between
groups at IUCAA and IIT Kanpur, has developed a method of estimating the CMB power spectrum solely
from multi-frequency data from WMAP that evades the modeling uncertainties involved in using extraneous
foreground maps. The Indian group carried out a completely model free removal of the foreground contamination and an independent estimation of the angular power spectrum from WMAP data releases shown in the
figure 3. Data archive sites such as the Legacy Archive of Microwave Background Analysis (LAMBDA) are
excellent up to date repository for any researcher seeking to work in this field from anywhere in the world.
The angular power spectrum of the Cosmic Microwave Background temperature fluctuations, C ` , have
become invaluable observables for constraining cosmological models. The position and amplitude of the
peaks and dips of the C` are sensitive to important cosmological parameters, such as, the relative density
(with respect to the critical density) of dark matter, Ωm ; cosmological constant, ΩΛ ; baryon content, ΩB ;
Hubble constant, H0 and deviation from flatness (curvature), ΩK . The measurements of the anisotropy in the
cosmic microwave background (CMB) over the past decade has led to ‘precision cosmology’. Observations
of the large scale structure in the distribution of galaxies, high redshift supernova, and more recently, CMB
polarization, have provided the required complementary information. The observation establish that the
space on cosmic scales is geometrically flat (ΩK = 0) to within 2%. The dominant energy content in
the present universe is a mysterious matter with negative pressure dubbed, dark energy or a cosmological
constant of about 73% (ΩΛ = 0.73), followed by cold non-baryonic dark matter about 23% (Ω m = 0.23) and
ordinary matter (baryons) account for only about 4% (ΩB = 0.04) of the matter budget. The exact numbers
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Figure 3: The exquisite temperature anisotropy data from the three years of data from WMAP satellite is
shown in the figures. Top: The top figure shows color coded full sky map (in Mollewide projection)of the
CMB temperature variations. The temperature variations are range between ±200µK with a r.m.s. of about
70µK. The angular resolution of features of the map is about a quarter of a degree. For comparison, the
first CMB anisotropy measurements in 1992 by the DMR instrument on board the COBE satellite produced
the same map at a much coarser resolution of 7 degrees. Bottom: The lower figure plots the angular power
spectrum from WMAP-1year (red) and WMAP-3 year (blue) data is shown. The solid line is the theoretical
prediction of the best fit cosmological model. The results shown in these figure have been obtained using
a novel, blind estimation method developed in India by R. Saha, P. Jain and T. Souradeep and is in good
agreement with that obtained by the WMAP team.
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are known with good statistical precision, but do systematically depend on the data-sets used and parameter
spaces of the cosmological models. Hence, in this rapidly moving field of research the current up to date
status of cosmological parameter estimates from joint analysis of CMB anisotropy and Large scale structure
(LSS) data is usually best to look up in the literature accompanying the most recent major experimental
results.
In addition to the temperature anisotropy, there is linear polarization information (Q and U Stokes parameters) imprinted on the CMB at last scattering surface. Thomson scattering generates CMB polarization
anisotropy at decoupling. This arises from the polarization dependence of the differential cross section. A
local quadrupole temperature anisotropy produces a net polarization, because of the cos 2 θ dependence of
the cross section. A net pattern of linear polarization is retained due to local quadrupole intensity anisotropy
of the CMB photon flux around the electrons at the surface of last scattering. The coordinate–free description distinguishes two kinds of polarization pattern on the sky by their different parities. In the spinor
approach, the even parity pattern is called the E–mode and the odd parity pattern the B–mode. With the
introduction of polarization, there are a total of 4 power spectra to determine: C `TT , C`TE , C`EE , C`BB ; parity
considerations eliminate the two other possible power spectra. While CMB temperature anisotropy can also
be generated during the propagation of the radiation from the last scattering surface, the CMB polarization
signal can be generated only the last scattering surface, where the optical depth transits from large to small
values. The polarization information complements the CMB temperature anisotropy by isolating the effect
at the last scattering surface from effects along the line of sight. Since the CMB polarization is sourced by
the anisotropy of the CMB at the surface of last scattering, the angular power spectra of temperature and
polarization are strongly linked to each other. For adiabatic initial perturbations, the acoustic peaks in the
polarization spectra are out of phase with that of the temperature.
The Degree Angular Scale Interferometer (DASI) first measured the CMB polarization spectrum over a
limited band of angular scales (multipole band l ∼ 200 − 440) in late 2002. The second data release from
WMAP in March 2006 was another milestone in CMB research that provided the first ‘all sky’ maps of
(E-mode) of CMB polarization. The DASI experiment recently published 3–year results of much refined
measurements. More recently, the BOOMERanG collaboration reports measurements of C `TT , C`TE and
C`EE . The main results indicated by the E-mode polarization measurements is that the acoustic peaks in the
polarization spectra are out of phase with that of the temperature. The stringent limits on the non-adiabatic
contribution to the primordial perturbations constrains the physics of the early universe.
The B-modes of CMB polarization are a very clean and direct probe of the energy scale of early universe
physics that generate the primordial metric perturbations. In the standard model, inflation generates both
(scalar) density perturbations and (tensor) gravitational wave perturbations. The relative amplitude of tensor
to scalar perturbations, r, sets the energy scale for inflation EI = 3.4 × 1016 Gev r 1/4 . Recent CMB
and LSS data alone puts an improved upper limit on the tensor to scalar ratio, r. A measurement of B–
mode polarization on large scales would give us this amplitude, and hence a direct determination of the
energy scale of inflation. The stochastic gravitational wave background from inflation is expected to exist on
cosmological scales down to terrestrial scales. This will be targeted by both CMB polarization experiments,
as well as, future GW observatories in space, such as LISA. The first CMB normalized GW spectra from
inflation using the COBE results was given by Varun Sahni and myself at IUCAA,in 1992 [5]. Figure 4
summarizes the current theoretical understanding, observational constraints and future possibilities for the
stochastic gravity wave background from inflation [3]. Besides being a generic prediction of inflation, the
cosmological gravity wave background from inflation would be a fundamental test of GR on cosmic scales
and the semi-classical behavior of gravity.
Besides precise determination of various parameters of the ‘standard’ cosmological model, observations
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Figure 4: The figure taken from Ref. [3, 4] shows the theoretical predictions and observational constraints
on primordial gravitational waves from inflation. The gravitational wave energy density per logarithmic frequency interval, (in units of the critical density) is plotted versus frequency. The shaded (blue) band labeled
‘minimally tuned’ represents the range predicted for simple inflation models with the minimal number of
parameters and tunings. The dashed curves have lower values of tensor contribution, r, that is possible with
more fine tuned inflationary scenarios. The currently existing experimental constraints shown are due to:
big bang nucleosynthesis (BBN), binary pulsars, and WMAP-1 (first year) with SDSS. Also shown are the
projections for LIGO (both LIGO-I, after one year running, and LIGO-II); LISA; and BBO (both initial
sensitivity, BBO-I, and after cross-correlating receivers, BBO-Corr). Also seen the projected sensitivity of a
future space mission for CMB polarization (CMBPol).
have also established some important basic tenets of cosmology and structure formation in the universe –
‘acausally’ correlated initial perturbations, adiabatic nature primordial density perturbations, gravitational
instability as the mechanism for structure formation. We have inferred a spatially flat universe where structures form by the gravitational evolution of nearly scale invariant, adiabatic perturbations, as expected from
inflation. The signature of primordial perturbations observed as the CMB anisotropy and polarization is the
most compelling evidence for new, possibly fundamental, physics in the early universe that underlie the scenario of inflation (or related alternatives). However, some fundamental ‘assumptions’ rooted in the paradigm
of inflation’ are still to be observationally established. Besides, there are deeper issues and exotic possibilities that no longer remain theoretical speculations, but come have now well within the grasp of cosmological
observations. These include cosmic topology, extra-dimensions, and violations of basic symmetries such as
Lorentz transformations. In order to detect the subtle signatures it is also important to identify and weed out
systematic effects such as the non-circularity of the beam in the acquisition and analysis of the CMB data.
These are some of the key issues addressed in the research work carried out by the CMB research group in
IUCAA [7].
The past few years have seen the emergence of a ‘concordant’ cosmological model that is consistent,
both, with observational constraints from the background evolution of the universe, as well as, that from
the formation of large scale structure in the distribution of matter in the universe. It is certainly fair to say
that the present edifice of the ‘standard’ cosmological models is robust. A set of foundation and pillars of
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cosmology have emerged and are each supported by a number of distinct observations [1]. The community
is now looking beyond the estimation of parameters of a working ‘standard’ model of cosmology. There is
increasing effort towards establishing the basic principles and assumptions. The feasibility and promise of
this ambitious goal is based on the grand success in the recent years with the CMB anisotropy measurements.
The measurement of CMB anisotropy will improve dramatically in the near future. Besides the periodic
release of WMAP data over six years, results expected to come in from a large number of other ongoing
experiments over the next decade. The detection CMB polarization by DASI in 2003 has opened a new
window that has been followed up a host of experiments. The Planck Surveyor mission of ESA due for
launch in mid-2008. In the next five years, we will have data from the eight years of the WMAP mission
and the upcoming ESA, Planck satellite. In the future, a dedicated CMB polarization mission has been listed
as a priority by both NASA (Beyond Einstein) and ESA (Cosmic Vision) in the time frame 2015-2020 [4].
These primarily target the B-mode polarization signature of gravity waves, and consequently, identify the
viable sectors in the space of inflationary parameters.
References
[1] J. P. Ostriker and T. Souradeep, Pramana, 63, 817, (2004).
[2] W. Hu and S. Dodelson, Ann. Rev. of Astron. and Astrophys. 40, 171 (2002). Also see online
articles at webpage of Wayne Hu at http://background.uchicago.edu/ and Ned Wright’s webpage
at http://www.astro.ucla.edu/∼wright/cosmolog.htm
[3] L. A. Boyle, P. J. Steinhardt & N. Turok, Phys. Rev. Lett. 96 111301 (2006).
[4] NASA/DOE/NSF Task force report on Cosmic Microwave Background research, 2005.
http://www.nsf.gov/mps/ast/tfcr.jsp (Also available at the Legacy Archive for Microwave Background Data analysis (LAMBDA) site http://lambda.gsfc.nasa.gov/)
[5] T. Souradeep and V. Sahni, Mod. Phys. Lett. A, 7,3541, (1992).
[6] R. Saha , P. Jain and T. Souradeep, Astrophys. J. Lett. 645, L89, (2006); T. Souradeep, R. Saha
and P. Jain, New Astronomy Reviews 50 854-860 (2006).
[7] T. Souradeep, Indian J. Phys. 80 1063 (2006); A. Hajian and T. Souradeep, Phys. Rev. D 75
123502 (2007); S. Basak, A. Hajian and T. Souradeep, Phys. Rev. D 74 021301(R) (2006);
T. Ghosh, A. Hajian and T. Souradeep, Phys. Rev. D 75, 083007 (2007); A. Shafieloo and
T. Souradeep, Phys Rev. D 70, 043523, (2004); A. Shafieloo and T. Souradeep, preprint,
arXiv:0709.1944 (2007); S. Mitra, A. S. Sengupta and T. Souradeep, Phys Rev. D70 103002,
(2004); S. Mitra, S. Ray, R. Saha, A. S. Sengupta and T. Souradeep, preprint, astro-ph/0702100
(2007).
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