Primordial Gravitational Waves and Cosmic Microwave Background Radiation
D. Baskaran, L. P. Grishchuk, W. Zhao
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A summary of presentations delivered at the OC1 parallel session "Primordial Gravitational Waves and the CMB" of the 12th Marcel Grossmann Meeting on General Relativity (Paris, 12-18 July 2009). To be published in the Proceedings of the MG12. 18 pages, 8 (colour) figures.
This is a summary of presentations delivered at the OC1 parallel session "Primordial Gravitational Waves and the CMB" of the 12th Marcel Grossmann meeting in Paris, July 2009. The reports and discussions demonstrated significant progress that was achieved in theory and observations. It appears that the existing data provide some indications of the presence of gravitational wave contribution to the CMB anisotropies, while ongoing and planned observational efforts are likely to convert these indications into more confident statements about the actual detection.
The General Relativity affirms that any field is a source of gravitational field, thus one should affirm that the energy of Cosmic Microwave Background (CMB) generated primordial gravitational waves. The present article shows that a gravitational wave with dimensionless amplitude $\sim 10^{-5}$ and large wave length $\sim 10$ megaparsecs shifts temperature of CMB radiation about of a part in $10^{5}$.
Circular ("V-mode") polarization is expected to be vanishing in the CMB, since it is not produced in Thomson scattering. However, considering that the conventional CMB anisotropies are generated via an early universe mechanism such as inflation or a bouncing scenario, it is possible that circular polarization could be primordially produced and survive to the surface of last scattering. We study this in detail, and find a large class of inflationary models that produce a nearly scale invariant spectrum of scalar V-mode anisotropies. We study the inflationary production and subsequent evolution …
Primordial magnetic fields (PMFs) create a large squeezed-type non-Gaussianity in tensor perturbation, which generates non-Gaussian temperature fluctuations in the cosmic microwave background (CMB). We for the first time derive an observational constraint on such a tensor non-Gaussianity from observed CMB maps. Analyzing temperature maps of the WMAP 7-year data, we find that such a tensor non-Gaussianity is consistent with zero. This gives an upper bound on PMF strength smoothed on $1 ~ {\rm Mpc}$ as $B_{1 ~ \rm Mpc} < 3.1 ~{\rm nG}$ at $95%$ C.L.
Primordial magnetic fields will generate non-Gaussian signals in the cosmic microwave background (CMB) as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. We compute a new measure of magnetic non-Gaussianity, the CMB trispectrum, on large angular scales, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of approximately a few times 10^{-29} and 10^{-19}, respectively. Observational limits on CMB non-Gaussianity from WMAP data…
Since the first limit on the (local) primordial non-Gaussianity parameter, fNL, was obtained from COBE data in 2002, observations of the CMB have been playing a central role in constraining the amplitudes of various forms of non-Gaussianity in primordial fluctuations. The current 68% limit from the 7-year WMAP data is fNL=32+/-21, and the Planck satellite is expected to reduce the uncertainty by a factor of four in a few years from now. If fNL>>1 is found by Planck with high statistical significance, all single-field models of inflation would be ruled out. Moreover, if the Planck satellite fin…
We review in a pedagogical way the present status of the impact of non-Gaussianity (NG) on the Cosmic Microwave Background (CMB) anisotropies. We first show how to set the initial conditions at second-order for the (gauge invariant) CMB anisotropies when some primordial NG is present. However, there are many sources of NG in CMB anisotropies, beyond the primordial one, which can contaminate the primordial signal. We mainly focus on the NG generated from the post-inflationary evolution of the CMB anisotropies at second-order in perturbation theory at large and small angular scales, such as the …
We calculate the cosmic microwave background bispectrum of vector modes induced from primordial magnetic fields. We take into account the full angular dependence of the bispectrum and discuss the amplitude and also the shape of the bispectrum in $\ell$ space. In the squeezed limit as $\ell_1 = \ell_2 \gg \ell_3$, we estimate a typical values of the normalized reduced bispectrum as $\ell_1(\ell_1 + 1)\ell_3(\ell_3+1)|b_{\ell_1\ell_2\ell_3}| \sim 2 \times 10^{-19}$, for the strength of the primordial magnetic field smoothed on $1 {\rm Mpc}$ scale $B_{1 \rm Mpc} = 4.7 \rm nG$ assuming a nearly sc…
Study of primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ with the cross-correlations between the scalar-induced gravitational waves and the cosmic microwave background
We propose an inflationary primordial feature model that can explain both the large and small-scale anomalies in the currently measured cosmic microwave background (CMB) anisotropy spectra, revealing a clip of adventurous history of the Universe during its primordial epoch. Although the model is currently statistically indistinguishable from the Standard Model, we show that future observations such as the Simons Observatory and LiteBIRD will complement each other in distinguishing the model differences due to their accurate E-mode polarization measurements, and the PICO mission, if funded, can…
Rotational invariance is a well-established feature of low-energy physics. Violations of this symmetry must be extremely small today, but could have been larger in earlier epochs. In this paper we examine the consequences of a small breaking of rotational invariance during the inflationary era when the primordial density fluctuations were generated. Assuming that a fixed-norm vector picked out a preferred direction during the inflationary era, we explore the imprint it would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes $<a_{lm}a…
Recently, the cross-correlation between $E$- and $B$-mode polarization of the cosmic microwave background (CMB), which is well explained by cosmic birefringence with rotation angle $β\approx 0.3$ deg, has been found in CMB polarization data. We carefully investigate the possibility of explaining the observed $EB$ correlation by the primordial chiral gravitational waves (CGWs), which can be generated in the parity-violating theories in the primordial Universe. We found that the CGWs scenario does not work due to the overproduction of the $BB$ auto-correlation which far exceeds the observed one …
We present a novel mechanism to generate the cosmic perturbation from evaporation of primordial black holes. A mass of a field is fluctuated if it is given by a vacuum expectation value of a light scalar field because of the quantum fluctuation during inflation. The fluctuated mass causes variations of the evaporation time of the primordial black holes. Therefore provided the primordial black holes dominate the universe when they evaporate, primordial cosmic perturbations are generated. We find that the amplitude of the large scale curvature perturbation generated in this scenario can be consi…
If primordial black holes (PBHs) form directly from inhomogeneities in the early Universe, then the number in the mass range $10^5 -10^{12}M_{\odot}$ is severely constrained by upper limits to the $μ$ distortion in the cosmic microwave background (CMB). This is because inhomogeneities on these scales will be dissipated by Silk damping in the redshift interval $5\times 10^4\lesssim z\lesssim2\times 10^6$. If the primordial fluctuations on a given mass scale have a Gaussian distribution and PBHs form on the high-$σ$ tail, as in the simplest scenarios, then the $μ$ constraints exclude PBHs in thi…
These lecture notes cover mainly three connected topics. In the first part we give a detailed treatment of cosmological perturbation theory. The second part is devoted to cosmological inflation and the generation of primordial fluctuations. In part three it will be shown how these initial perturbation evolve and produce the temperature anisotropies of the cosmic microwave background radiation. Comparing the theoretical prediction for the angular power spectrum with the increasingly accurate observations provides important cosmological information (cosmological parameters, initial conditions).
We study the effect of primordial magnetic fields (PMFs) on the anisotropies of the cosmic microwave background (CMB). We assume the spectrum of PMFs is described by log-normal distribution which has a characteristic scale, rather than power-law spectrum. This scale is expected to reflect the generation mechanisms and our analysis is complementary to previous studies with power-law spectrum. We calculate power spectra of energy density and Lorentz force of the log-normal PMFs, and then calculate CMB temperature and polarization angular power spectra from scalar, vector, and tensor modes of per…
The observability of primordial cosmic fluctuations does not require a geometric horizon $H^{-1}$, which is exceeded temporarily by the wavelength of fluctuations. The primordial information can be protected against later thermal washout even if all relevant wavelengths remain smaller than $H^{-1}$. This is demonstrated by formulating the equations governing the cosmic fluctuations in a form that is manifestly invariant under conformal field transformations of the metric. Beyond the field equations this holds for the defining equation for the correlation function, as expressed by the inverse o…
Using the full radiation transfer function, we numerically calculate the CMB angular bispectrum seeded by the compensated magnetic scalar density mode. We find that, for the string inspired primordial magnetic fields characterized by index $n_B=-2.9$ and mean-field amplitude $B_{\lam}=9{\rm nG}$, the angular bispectrum is dominated by two primordial magnetic shapes. The first magnetic shape looks similar to the one from local-type primordial curvature perturbations, so both the amplitude and profile of the Komatsu-Spergel estimator (reduced bispectrum) seeded by this shape are almost the same …
Measuring the deviation from scale invariance of the primordial power spectrum is a critical test of inflation. In this paper we reconstruct the shape of the primordial power spectrum of curvature perturbations from the cosmic microwave background data, including the 7-year Wilkinson Microwave Anisotropy Probe data and the Atacama Cosmology Telescope 148 GHz data, by using a binning method of a cubic spline interpolation in log-log space. We find that the power-law spectrum is preferred by the data and that the Harrison-Zel'dovich spectrum is disfavored at 95% confidence level. These conclusio…
We suggest a general relation between the position of the cosmic microwave background temperature power spectrum peaks and the inflationary slow roll parameter $ε$. This relation is based on interpreting the variable setting the position of the peaks as the quantum distance between the end of inflation and recombination. This distance is determined by the primordial cosmological Fisher information introduced in arXiv:2002.04294. The observational constraints set by cosmic microwave background temperature data lead to a very stringent prediction for the value of the tensor-to-scalar ratio: $r=0…
Primordial gravitational waves (GWs) with frequencies > 10^{-15} Hz contribute to the radiation density of the Universe at the time of decoupling of the cosmic microwave background (CMB). The effects of this GW background on the CMB and matter power spectra are identical to those due to massless neutrinos, unless the initial density-perturbation amplitude for the gravitational-wave gas is non-adiabatic, as may occur if such GWs are produced during inflation or some post-inflation phase transition. In either case, current observations provide a constraint to the GW amplitude that competes with …
Temperature and polarization variations across the microwave sky include the fingerprints of quantum fluctuations in the early universe. They may soon reveal physics at unprecedented energy scales.
Both the Wilkinson Microwave Anisotropy Probe (WMAP) and Planck observations reported the hemispherical asymmetry of the cosmic microwave background (CMB) temperature fluctuation. The hemispherical asymmetry might be stemmed from the primordial statistical anisotropy during the inflationary era of the universe. In this paper, we study possible implications of the primordial power spectra with dipolar anisotropy on the CMB temperature fluctuation and polarizations. We explicitly show that the statistical dipolar anisotropy may induce the off-diagonal (\(\ell'\neq\ell\)) $TT$, $EE$, $BB$, and $T…
In this work we study the imprints of a primordial cosmic string on inflationary power spectrum. Cosmic string induces two distinct contributions on curvature perturbations power spectrum. The first type of correction respects the translation invariance while violating isotropy. This generates quadrupolar statistical anisotropy in CMB maps which is constrained by the Planck data. The second contribution breaks both homogeneity and isotropy, generating a dipolar power asymmetry in variance of temperature fluctuations with its amplitude falling on small scales. We show that the strongest constra…
We consider the imprint of superradiant instabilities of nonevaporating primordial black holes (PBHs) on the spectrum of the cosmic microwave background (CMB). In the radiation dominated era, PBHs are surrounded by a roughly homogeneous cosmic plasma which endows photons with an effective mass through the plasma frequency. In this setting, spinning PBHs are unstable to a spontaneous spindown through the well-known "black-hole bomb" mechanism. At linear level, the photon density is trapped by the effective photon mass and grows exponentially in time due to superradiance. As the plasma density d…
It is commonly assumed that the stochastic background of gravitational waves on cosmological scales follows an almost scale-independent power spectrum, as generically predicted by the inflationary paradigm. However, it is not inconceivable that the spectrum could have strongly scale-dependent features, generated, e.g., via transient dynamics of spectator axion-gauge fields during inflation. Using the temperature and polarisation maps from the \textit{Planck} and BICEP/Keck datasets, we search for such features, taking the example of a log-normal bump in the primordial tensor spectrum at CMB sc…
We consider a modification of the Heisenberg algebra with the non-vanishing commutator of scalar field operators. We then identify the scalar field with the second quantized inflaton fluctuation and calculate effects of microcausality violation on the temperature anisotropy of cosmic microwave background radiation.
A cosmological gauge field with isotropic stress-energy introduces parity violation into the behavior of gravitational waves. We show that a primordial spectrum of inflationary gravitational waves develops a preferred handedness, left- or right-circularly polarized, depending on the abundance and coupling of the gauge field during the radiation era. A modest abundance of the gauge field would induce parity-violating correlations of the cosmic microwave background temperature and polarization patterns that could be detected by current and future experiments.
We investigate the formation of primordial black holes (PBHs) from the collapse of spherically symmetric domain wall bubbles, which spontaneously nucleate via quantum tunneling during inflation. Since the tension of domain walls changes with time and so domain walls nucleate in a short time interval, the mass function of PBHs in general has a spike-like structure. In contrast to models in which PBHs produced from overdense regions, our model avoids the uncertainties of PBHs production mechanism. PBHs from domain walls with mass around $10^{20}\mathrm{g}$ may constitute all dark matter, those w…
Understanding the interaction of primordial gravitational waves (GWs) with the Cosmic Microwave Background (CMB) plasma is important for observational cosmology. In this article, we provide an analysis of an effect apparently overlooked as yet. We consider a single free electric charge and suppose that it can be agitated by primordial GWs propagating through the CMB plasma, resulting in periodic, regular motion along particular directions. Light reflected by the charge will be partially polarized, and this will imprint a characteristic pattern on the CMB. We study this effect by considering a …
We discuss a minimal canonical modification of electrodynamics in order to account for ultraviolet Lorentz violating effects. This modification creates a birefringence that rotates the polarization planes from different directions. Such effects might be detectable in the anisotropic polarization of the Cosmic Microwave Background radiation.
We estimate the B-polarisation induced in the Cosmic Microwave Background by the non-linear evolution of density perturbations. Using the second-order Boltzmann code SONG, our analysis incorporates, for the first time, all physical effects at recombination. We also include novel contributions from the redshift part of the Boltzmann equation and from the bolometric definition of the temperature in the presence of polarisation. The remaining line-of-sight terms (lensing and time-delay) have previously been studied and must be calculated non-perturbatively. The intrinsic B-mode polarisation is pr…
We briefly review certain aspects of cosmic microwave background anisotropies as generated in passive and active models of structure formation. We then focus on cosmic strings based models and discuss their status in the light of current high-resolution observations from the BOOMERanG, MAXIMA and DASI collaborations. Upcoming megapixel experiments will have the potential to look for non-Gaussian features in the CMB temperature maps with unprecedented accuracy. We therefore devote the last part of this review to treat the non-Gaussianity of the microwave background and present a method for comp…
The primordial curvature fluctuation spectrum is reconstructed by the cosmic inversion method using the five-year WMAP data of the cosmic microwave background temperature anisotropy. We apply the covariance matrix analysis and decompose the reconstructed spectrum into statistically independent band-powers. The statistically significant deviation from a simple power-law spectrum suggested by the analysis of the first-year data is not found in the five-year data except possibly at one point near the border of the wavenumber domain where accurate reconstruction is possible.
The primordial curvature fluctuation spectrum is reconstructed by the maximum likelihood reconstruction method using the five-year Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background temperature anisotropy. We apply the covariance matrix analysis and decompose the reconstructed spectrum into statistically independent band-powers. The prominent peak off a simple power-law spectrum found in our previous analysis turn out to be a $3.3σ$ deviation. From the statistics of primordial spectra reconstructed from mock observations, the probability that a primordial spectrum inc…
The contribution of gravitational wave (tensor metric) and energy density (scalar metric) fluctuations to the cosmic microwave background polarization is computed by numerically solving the relativistic radiation transfer equations. We find that the tensor contribution is significant only at large angular scales (multipoles $\ell \lta 40$). For standard recombination, the tensor contribution can dominate at $\ell \lta 40$; however, the effect would be difficult to detect since the total (scalar plus tensor) polarization is $< 1$\%. For models with late reionization, the total large angular sca…
Standard D-term inflation is studied in the framework of supergravity. D-term inflation produces cosmic strings, however it can still be compatible with CMB measurements without invoking any new physics. The cosmic strings contribution to the CMB data is not constant, nor dominant, contrary to some previous results. Using current CMB measurements, the free parameters (gauge and superpotential couplings, as well as the Fayet-Iliopoulos term) of D-term inflation are constrained.
We describe a new code to search for signatures of cosmic strings in cosmic microwave anisotropy maps. The code implements the Canny Algorithm, an edge detection algorithm designed to search for the lines of large gradients in maps. Such a gradient signature which is coherent in position space is produced by cosmic strings via the Kaiser-Stebbins effect. We test the power of our new code to set limits on the tension of the cosmic strings by analyzing simulated data with and without cosmic strings. We compare maps with a pure Gaussian scale-invariant power spectrum with maps which have a contri…
We consider the observational constraints from the detection of antiprotons in the Galaxy on the amount of Primordial Black Holes (PBH) produced from primordial power spectra with a bumpy mass variance. Though essentially equivalent at the present time to the constraints from the diffuse $γ$-ray background, they allow a widely independent approach and they should improve sensibly in the nearby future. We discuss the resulting constraints on inflationary parameters using a Broken Scale Invariance (BSI) model as a concrete example.
It has been shown that the spectrum of quantum gravity contains at least two new modes in addition to the massless graviton: a massive spin-0 and a massive spin-2. We calculate their power spectrum during inflation and we argue that they could leave an imprint in the cosmic microwave background should their masses be below the inflationary scale.
We offer a method of calculating the source term in the line-of-sight integral for cosmic microwave background anisotropies without using a truncated partial-wave expansion in the Boltzmann hierarchy.
We point out that in the context of ``two-metric'' theories of gravity there is the possibility that cosmic defects will produce a spectrum of primordial adiabatic density perturbations. This will happen when the speed characterising the defect-producing scalar field is much larger than the speed characterising gravity and all standard model particles. This model will exactly mimic the standard predictions of inflationary models, with the exception of a small non-Gaussian signal which could be detected by future experiments. We briefly discuss defect evolution in these scenarios and analyze th…
There have been vigorous research attempts to test various modified gravity theories by usingphysics of the cosmic microwave background (CMB). Meanwhile, symmetry breaking such as Higgsmechanism is one of the most important phenomena in physics but there have been not so muchresearches to make them contact with cosmological observations. In this article, with the CMBpower spectra we try to distinguish two different scenarios of spontaneous symmetry breaking inprimordial era of the universe. The first model is based on a broken symmetric theory of gravity,which was suggested by A. Zee in 1979. …
A violation of the reciprocity relation, which induces a violation of the distance duality relation, reflects itself in a change in the normalisation of the cosmic microwave spectrum in such a way that its spectrum is grey. We show that existing observational constraints imply that the reciprocity relation cannot be violated by more than 0.01% between decoupling and today. We compare this effect to other sources of violation of the distance duality relations which induce spectral distortion of the cosmic microwave background spectrum.
We investigate the effect of non-evaporating primordial black holes (PBHs) on the ionization and thermal history of the universe. X-rays emitted by gas accretion onto PBHs modify the cosmic recombination history, producing measurable effects on the spectrum and anisotropies of the Cosmic Microwave Background (CMB). Using the third-year WMAP data and FIRAS data we improve existing upper limits on the abundance of PBHs with masses >0.1 Msun by several orders of magnitude. Fitting WMAP3 data with cosmological models that do not allow for non-standard recombination histories, as produced by PBHs o…
We show that in a pioneering paper by Polnarev and Zembowicz, some conclusions concerning the characteristics of the Turok-strings are generally not correct. In addition we show that the probability of string collapse given there, is off by a large prefactor (~1000).
Primordial black holes with a narrow mass range are regarded as a nonrelativistic fluid component with an equation of state for dust. The impact of the black hole evaporation on the dynamics of the early universe is studied by resorting to a two-fluid model. We find periods of intense radiation reheating in the initial and final stages of the evaporation.
We study Newtonian cosmological perturbation theory from a field theoretical point of view. We derive a path integral representation for the cosmological evolution of stochastic fluctuations. Our main result is the closed form of the generating functional valid for any initial statistics. Moreover, we extend the renormalization group method proposed by Mataresse and Pietroni to the case of primordial non-Gaussian density and velocity fluctuations. As an application, we calculate the nonlinear propagator and examine how the non-Gaussianity affects the memory of cosmic fields to their initial co…
Recent observations of the cosmic microwave background (CMB) have extended the measured power spectrum to higher multipoles $l\gtrsim$1000, and there appears to be possible evidence for excess power on small angular scales. The primordial magnetic field (PMF) can strongly affect the CMB power spectrum and the formation of large scale structure. In this paper, we calculate the CMB temperature anisotropies generated by including a power-law magnetic field at the photon last-scattering surface (PLSS). We then deduce an upper limit on the PMF based on our theoretical analysis of the power excess o…
We discuss the inflationary production of magnetic seeds for the galactic dynamo through the photon-graviphoton mixing typical of extended models of local supersymmetry. An analisys of the allowed region in parameter space shows that such a mechanism is compatible with existing phenomenological bounds on the vector mass and on the mixing parameter, but requires a large enough mixing that seems difficult to implement naturally in the context of a minimal supersymmetric scenario.
Field self-interactions are at the origin of the non-linearities inherent to General Relativity. We study their effects on the Cosmic Microwave Background anisotropies. We find that they can reduce or alleviate the need for dark matter and dark energy in the description of the Cosmic Microwave Background power spectrum.
We show the existence of spatially homogeneous but anisotropic cosmological models whose cosmic microwave background temperature is exactly isotropic at one instant of time but whose rate of expansion is highly anisotropic. The existence of these models shows that the observation of a highly isotropic cosmic microwave background temperature cannot alone be used to infer that the universe is close to a Friedmann-Lemaitre model.
The cosmological magnetic field is one of the important physical quantities which affect strongly the cosmic microwave background (CMB) power spectrum. Recent CMB observations have been extended to higher multipoles $l\gtrsim$1000, and they resultantly exhibit an excess power than the standard model prediction in cosmological theory which best fits the Wilkinson Microwave Anisotropy Probe (WMAP) data at lower multipoles $l\lesssim$900. We calculate the CMB temperature anisotropies generated by the power-law magnetic field at the last scattering surface (LSS) in order to remove the tension betw…
