Red Tilt Research Articles

Breaking of spatial diffeomorphism invariance, inflation and the spectrum of cosmological perturbations

Standard inflationary models yield a characteristic signature of a primordial power spectrum with a red tensor and scalar tilt. Nevertheless, Cannone et al. [1] recently suggested that, by breaking the assumption of spatial diffeomorphism invariance in the context of the effective field theory of inflation, a blue tensor spectrum can be achieved without violating the Null Energy Condition. In this context, we explore in which cases the inflationary model of [2] can yield a blue tilt of the tensor modes along with a red tilt in the scalar spectrum. Ultimately, we analyze under which conditions the model of [3] can reproduce the specific consistency relation of String Gas Cosmology.

A ΛCDM bounce scenario

We study a contracting universe composed of cold dark matter and radiation, and with a positive cosmological constant. As is well known from standard cosmological perturbation theory, under the assumption of initial quantum vacuum fluctuations the Fourier modes of the comoving curvature perturbation that exit the (sound) Hubble radius in such a contracting universe at a time of matter-domination will be nearly scale-invariant. Furthermore, the modes that exit the (sound) Hubble radius when the effective equation of state is slightly negative due to the cosmological constant will have a slight red tilt, in agreement with observations. We assume that loop quantum cosmology captures the correct high-curvature dynamics of the space-time, and this ensures that the big-bang singularity is resolved and is replaced by a bounce. We calculate the evolution of the perturbations through the bounce and find that they remain nearly scale-invariant. We also show that the amplitude of the scalar perturbations in this cosmology depends on a combination of the sound speed of cold dark matter, the Hubble rate in the contracting branch at the time of equality of the energy densities of cold dark matter and radiation, and the curvature scale that the loop quantum cosmology bounce occurs at. Importantly, as this scenario predicts a positive running of the scalar index, observations can potentially differentiate between it and inflationary models. Finally, for a small sound speed of cold dark matter, this scenario predicts a small tensor-to-scalar ratio.

Closed string thermodynamics and a blue tensor spectrum

The BICEP-2 team has reported the detection of primordial cosmic microwave background B-mode polarization, with hints of a suppression of power at large angular scales relative to smaller scales. Provided that the B-mode polarization is due to primordial gravitational waves, this might imply a blue tilt of the primordial gravitational wave spectrum. Such a tilt would be incompatible with standard inflationary models, although it was predicted some years ago in the context of a mechanism that thermally generates the primordial perturbations through a Hagedorn phase of string cosmology. The purpose of this note is to encourage greater scrutiny of the data with priors informed by a model that is immediately falsifiable, but which \textit{predicts} features that might be favoured by the data-- namely a blue tensor tilt with an induced and complimentary red tilt to the scalar spectrum, with a naturally large tensor to scalar ratio that relates to both.

Cosmological parameter fittings with the BICEP2 data

Combining the latest Planck, Wilkinson Microwave Anisotropy Probe (WMAP), and baryon acoustic oscillation (BAO) data, we exploit the recent cosmic microwave background (CMB) B-mode power spectra data released by the BICEP2 collaboration to constrain the cosmological parameters of the LCDM model, especially the primordial power spectra parameters of the scalar and the tensor modes, n s , α s , r, n t . We obtain constraints on the parameters for a lensed LCDM model using the Markov Chain Monte Carlo (MCMC) technique, the marginalized 68% bounds are r = 0.1043 +0.0307−0.0914 , n s = 0.9617 +0.0061−0.0061 , α s = −0.0175 +0.0105−0.0097 , n t = 0.5198 +0.4515−0.4579 .We find that a blue tilt for n t is favored slightly, but it is still well consistent with flat or even red tilt. Our r value is slightly smaller than the one obtained by the BICEP group, in that we permit n t as a free parameter without imposing the single-field slow roll inflation consistency relation. When we impose this relation, then r = 0.2130 +0.0446−0.0609 . For most other parameters, the best fit values and measurement errors are not altered significantly by the introduction of the BICEP2 data.

Exploring bouncing cosmologies with cosmological surveys

In light of the recent observational data coming from the sky we have two significant directions in the field of theoretical cosmology recently. First, we are now able to make use of present observations, such as the Planck and BICEP2 data, to examine theoretical predictions from the standard inflationary $\Lambda$CDM which were made decades of years ago. Second, we can search for new cosmological signatures as a way to explore physics beyond the standard cosmic paradigm. In particular, a subset of early universe models admit a nonsingular bouncing solution that attempts to address the issue of the big bang singularity. These models have achieved a series of considerable developments in recent years, in particular in their perturbative frameworks, which made brand-new predictions of cosmological signatures that could be visible in current and forthcoming observations. In this article we present two representative paradigms of very early universe physics. The first is the so-called new matter (or matter-ekpyrotic) bounce scenario in which the universe starts with a matter-dominated contraction phase and transitions into an ekpyrotic phase. In the setting of this paradigm, we propose some possible mechanisms of generating a red tilt for primordial curvature perturbations and confront its general predictions with recent cosmological observations. The second is the matter-bounce inflation scenario which can be viewed as an extension of inflationary cosmology with a matter contraction before inflation. We present a class of possible model constructions and review its implications on the current CMB experiments. Last, we review the significant achievements of these paradigms beyond the inflationary $\Lambda$CDM model, which we expect to shed new light on the direction of observational cosmology in the next decade years.

COLOR-MAGNITUDE RELATIONS WITHIN GLOBULAR CLUSTER SYSTEMS OF GIANT ELLIPTICAL GALAXIES: THE EFFECTS OF GLOBULAR CLUSTER MASS LOSS AND THE STELLAR INITIAL MASS FUNCTION

Several recent studies have provided evidence for a `bottom-heavy' stellar initial mass function (IMF) in massive elliptical galaxies. Here we investigate the influence of the IMF shape on the recently discovered color-magnitude relation (CMR) among globular clusters (GCs) in such galaxies. To this end we use calculations of GC mass loss due to stellar and dynamical evolution to evaluate (i) the shapes of stellar mass functions in GCs after 12 Gyr of evolution as a function of current GC mass along with their effects on integrated-light colors and mass-to-light ratios, and (ii) their impact on the effects of GC self-enrichment using the 2009 `reference' model of Bailin & Harris. As to the class of metal-poor GCs, we find the observed shape of the CMR (often referred to as the `blue tilt') to be very well reproduced by Bailin & Harris' reference self-enrichment model once 12 Gyr of GC mass loss is taken into account. The influence of the IMF on this result is found to be insignificant. However, we find that the observed CMR among the class of metal-rich GCs (the `red tilt') can only be adequately reproduced if the IMF was bottom-heavy (e.g., $-3.0 <~ \alpha <~ -2.3$ in $dN/dM \propto M^{\alpha}$), which causes the stellar mass function at subsolar masses to depend relatively strongly on GC mass. This constitutes additional evidence that the metal-rich stellar populations in giant elliptical galaxies were formed with a bottom-heavy IMF.

Reconstruction of broad features in the primordial spectrum and inflaton potential from Planck

With the recently published Cosmic Microwave Background data from Planck we address the optimized binning of the primordial power spectrum.As an important modification to the usual binning of the primordial spectrum, along with the spectral amplitude of the bins, we allow the position of the bins also to vary. This technique enables us to address the location of the possible broad physical features in the primordial spectrum with relatively smaller number of bins compared to the analysis performed earlier. This approach is in fact a reconstruction method looking for broad features in the primordial spectrum and avoiding fitting noise in the data. Performing Markov Chain Monte Carlo analysis we present samples of the allowed primordial spectra with broad features consistent with Planck data. To test how realistic it is to have step-like features in primordial spectrum we revisit an inflationary model, proposed by A. A. Starobinsky which can address the similar features obtained from the binning of the spectrum. Using the publicly available code BINGO, we numerically calculate the local fNL for this model in equilateral and arbitrary triangular configurations of wavevectors and show that the obtained non-Gaussianity for this model is consistent with Planck results. In this paper we have also considered different spectral tilts at different bins to identify the cosmological scale that the spectral index needs to have a red tilt and it is interesting to report that spectral index cannot be well constrained up to k ≈ 0.01Mpc−1.

Thermal power spectrum in the CFT driven cosmology

We present an overview of the recently suggested cosmological model driven by conformal field theory (CFT) with the initial conditions in the form of the microcanonical density matrix. In particular, we discuss the origin of inflationary stage in this model and a novel feature — the thermal nature of the primordial power spectrum of the CMB anisotropy. The relevant effect of ``temperature of the relic temperature anisotropy'' can be responsible for a thermal contribution to the red tilt of this spectrum, additional to its conventional vacuum component. The amplification of this effect due to recently established a-theorem in CFT is briefly discussed.

Confronting brane inflation with Planck and pre-Planck data

In this paper, we compare brane inflation models with the Planck data and the pre-Planck data (which combines WAMP, ACT, SPT, BAO and ${H}_{0}$ data). The Planck data prefer a spectral index less than unity at more than $5\ensuremath{\sigma}$ confidence level, and a running of the spectral index at around $2\ensuremath{\sigma}$ confidence level. We find that the KKLMMT model can survive at the level of $2\ensuremath{\sigma}$ only if the parameter $\ensuremath{\beta}$ (the conformal coupling between the Hubble parameter and the inflaton) is less than $\mathcal{O}({10}^{\ensuremath{-}3})$, which indicates a certain level of fine-tuning. The IR DBI model can provide a slightly larger negative running of spectral index and red tilt, but in order to be consistent with the non-Gaussianity constraints from Planck, its parameter also needs fine-tuning at some level.

The matter bounce scenario in loop quantum cosmology

In the matter bounce scenario, a dust-dominatedcontracting space-time generates scale-invariantperturbations that, assuming a nonsingularbouncing cosmology, propagate to the expandingbranch and set appropriate initial conditionsfor the radiation-dominated era. Since thisscenario depends on the presence of a bounce,it seems appropriate to consider it in thecontext of loop quantum cosmology where a bouncinguniverse naturally arises. For a pressurelesscollapsing universe in loop quantum cosmology, thepredicted power spectrum of the scalar perturbationsafter the bounce is scale-invariant and the tensorto scalar ratio is negligibly small. A slight redtilt can be given to the scale-invariance ofthe scalar perturbations by a scalar field whoseequation of state is P = −ϵρ, whereϵ is a small positive number. Then, thepower spectrum for tensor perturbations is alsoalmost scale-invariant with the same red tilt asthe scalar perturbations, and the tensor to scalarratio is expected to be r ≈ 9 × 10−4.Finally, for the predicted amplitude of the scalarperturbations to agree with observations, the criticaldensity in loop quantum cosmology must be of the orderρc ∼ 10−9ρPl.

Cosmology on compact and stable supergravity background

We propose a cosmological model of D3-brane universe on compact and stable supergravity background of wrapped D7-branes in type IIB string theory previously argued to be dual to pure N=1 SU(N) gauge theory in four dimensions. A model universe of order Planck size near the UV boundary dynamically flows toward the IR with constant total energy density and accelerating expansion followed by smooth transition to decelerating expansion and collides with the wrapped D7-branes at the IR boundary. The model addresses the horizon and flatness problems with most of the expansion produced during the decelerating expansion phase. The inflationary scenario is used to generate sources of inhomogeneities in the cosmic microwave background radiation and seeds for large scale structure formation from quantum fluctuations which exit the Hubble radius early during the accelerating expansion phase and the model addresses the inhomogeneity problem with red tilt in the power spectrum. We propose that the kinetic energy of the model universe is converted to matter and radiation by the collision followed by formation of baryons that stabilizes the model universe against gravitational force from the background at a finite distance from the IR boundary with the wrapped D7-branes serving as sources of color. Friedmann evolution then takes over with a positive cosmological constant term coming from the remaining potential energy density which is interpreted as dark energy. The magnitude of dark energy density is smaller than the total energy density during the flow by a ratio of the scale factor when the model universe appears in the UV to the scale factor at the moment of collision and stays constant while the matter-radiation density falls during Friedmann expansion.

On suppression of topological transitions in quantum gravity

We discuss the effect of dynamical suppression for a special class of topological configurations in cosmology, which occur in Euclidean quantum gravity (EQG) when the latter is viewed as the derivative of the physical theory in the Lorentzian signature spacetime. At the topological level EQG inherits from the Lorentzian theory the arrow of time and incorporates special junction conditions on quantum fields whose quantum fluctuations make the contribution of such topologies vanishing. This effect is more general than the recently suggested conformal mechanism of suppression of vacuum no-boundary instantons in the microcanonical statistical sum of quantum cosmology driven by a conformal field theory (CFT). In contrast to conformal properties of the CFT driven cosmology, this effect is based only on short-distance behavior of local boson fields and Pauli principle for fermions. Application of this effect in the CFT cosmology treated as initial conditions for inflationary Universe suggests the thermal nature of the primordial power spectrum of the CMB anisotropy. This can be responsible for a thermal contribution to the red tilt of this spectrum, additional to its conventional vacuum component.

Red spectral tilt and observable gravity waves in shifted hybrid inflation

We consider supersymmetric shifted hybrid inflation models with a red-tilted scalar spectral index ${n}_{s}$ in agreement with the WMAP 7-yr central value. If nonminimal supergravity corrections are included, these models can also support a tensor-to-scalar ratio as large as $r\ensuremath{\simeq}0.02$, which may be observable by the Planck Satellite. In contrast to the standard supersymmetric hybrid inflation scenario, topological defects produced via gauge symmetry breaking are inflated away in the shifted version of the theory.

Tensor tilt from primordial B modes

A primordial cosmic microwave background B-mode is widely considered a "smoking gun" signature of an early period of inflationary expansion. However, competing theories of the origin of structure, including string gases and bouncing cosmologies, also produce primordial tensor perturbations that give rise to a B-mode. These models can be differentiated by the scale dependence of their tensor spectra: inflation predicts a red tilt ($n_T<0$), string gases and loop quantum cosmology predict a blue tilt ($n_T>0$), while a nonsingular matter bounce gives zero tilt ($n_T=0$). We perform a Bayesian analysis to determine how far $|n_T|$ must deviate from zero before a tilt can be detected with current and future B-mode experiments. We find that Planck in conjunction with QUIET (II) will decisively detect $n_T \neq 0$ if $|n_T| > 0.3$, too large to distinguish either single field inflation or string gases from the case $n_T=0$. While a future mission like CMBPol will offer improvement, only an ideal satellite mission will be capable of providing sufficient Bayesian evidence to distinguish between each model considered.

Inflation in entropic cosmology: Primordial perturbations and non-Gaussianities

We investigate thermal inflation in double-screen entropic cosmology. We find that its realization is general, resulting from the system evolution from non-equilibrium to equilibrium. Furthermore, going beyond the background evolution, we study the primordial curvature perturbations arising from the universe interior, as well as from the thermal fluctuations generated on the holographic screens. We show that the power spectrum is nearly scale-invariant with a red tilt, while the tensor-to-scalar ratio is in agreement with observations. Finally, we examine the non-Gaussianities of primordial curvature perturbations, and we find that a sizable value of the non-linearity parameter is possible due to holographic statistics on the outer screen.

Noncanonical kinetic terms and the tilt of the power spectrum

We argue that in models of inflation with two scalar fields and noncanonical kinetic terms there is a possibility of obtaining a red tilt of the power spectrum of curvature perturbations from noncanonicality-induced interactions between the curvature and isocurvature perturbations. We describe an extremely simple model realizing this idea, study numerically its predictions for the perturbations, and discuss applications in realistic scenarios of inflation. We discuss to what extent in this model the scale of the inflationary potential can be decoupled from the amplitude of the density fluctuations.

Single-field inflation constraints from CMB and SDSS data

We present constraints on canonical single-field inflation derived from WMAP five year, ACBAR, QUAD, BICEP data combined with the halo power spectrum from SDSS LRG7. Models with a non-scale-invariant spectrum and a red tilt nS < 1 are now preferred over the Harrison-Zel'dovich model (nS = 1, tensor-to-scalar ratio r = 0) at high significance. Assuming no running of the spectral indices, we derive constraints on the parameters (nS, r) and compare our results with the predictions of simple inflationary models. The marginalised credible intervals read nS = 0.962+0.028−0.026 and r < 0.17 (95% confidence level). With respect to previous analyses, the portion of the 68% c.l. contours compatible with potentials which are concave in the observable region becomes even smaller, but the quadratic potential model remains inside the 95% c.l. contours. We demonstrate that these results are robust to changes in the datasets considered and in the theoretical assumptions made. We then consider a non-vanishing running of the spectral indices by employing different methods, non-parametric but approximate, or parametric but exact. With our combination of CMB and LSS data, running models are preferred over power-law models only by a Δχ2 ≃ 5.8, allowing inflationary stages producing a sizable negative running −0.063+0.061−0.049 and larger tensor-scalar ratio r < 0.33 at the 95% c.l. This requires large values of the third derivative of the inflaton potential within the observable range. We derive bounds on this derivative under the assumption that the inflaton potential can be approximated as a third order polynomial within the observable range.

Accelerating the universe with gravitational waves

Inflation generically produces primordial gravitational waves with a red spectral tilt. In this paper we calculate the backreaction produced by these gravitational waves on the expansion of the universe. We find that in radiation domination the backreaction acts as a relativistic fluid, while in matter domination a small dark energy emerges with an equation of state weff ≈ −8/9.

Multi-field inflation with a random potential

Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian-like motion with a drift in the D-dimensional field space, allowing entropic perturbation modes to continuously and randomly feed into the adiabatic mode. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario where the stochastic scatterings are frequent but mild, the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, in which the coarse-grained motion of the inflaton is significantly slowed down by the scatterings, leads to rich phenomenologies. The power spectrum exhibits primordial fluctuations on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and have been smoothed out by binning of data points. With more data coming in the future, we expect these features can be detected or falsified. On the other hand the tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced by the large ratio of the Brownian-like motion speed over the drift speed. In addition a large negative running of the power spectral index is possible.Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, and is negligible in the weakly random scenario. However, non-Gaussianity can possibly be enhanced by resonant effects in the strongly random scenario or arise from the entropic perturbations during the onset of (p)reheating if the background inflaton trajectory exhibits particular properties. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.

COLOR BIMODALITY IN M87 GLOBULAR CLUSTERS

We present an analysis of a 50 orbit HST ACS observation of the M87 globular cluster system. We use the extraordinary depth of this dataset to test whether the colors and magnitudes show evidence for a mass-metallicity relation in globular cluster populations. We find only a weak or absent relation between the colors and magnitudes of the metal poor subpopulation of globular clusters. The weakness or absence of a color-magnitude relation is established over a wide range in luminosity from $M_V=-11$ to $M_V=-6$, encompassing most of the M87 globular clusters. The constancy of the colors of the metal-poor subpopulation seen in our 50 orbit observation is in contrast to suggestions from single orbit ACS data that the metal-poor globular clusters in M87 and several other galaxies show a "blue tilt." The formal best fit for the mass-metallicity relation for the metal-poor subpopulation in our much deeper data is $Z\propto M^{0.08\pm0.05}$. Our analysis of these data also shows a possible small "red tilt" in the metal-rich globular cluster subpopulation. While either of these small tilts may be real, they may also illustrate the limit to which mass-metallicity relations can be determined, even in such extraordinarily deep data. We specifically test for a wide range of systematic effects and find that while small tilts cannot be confirmed or rejected, the data place a strong upper limit to any tilt of $|0.20|\pm0.05$. This upper limit is much smaller than some earlier claims from single orbit data, and strongly limits self-enrichment within globular clusters. This mass-metallicity relation for globular clusters is also shallower than the relation for galaxies, suggesting that the formation mechanisms for these two types of objects are different.