Inflation after Planck and BICEP2

We discuss the inflationary paradigm, how it can be tested, and how various models of inflation fare in the light of data from Planck and BICEP2. We introduce inflation and reheating, and discuss temperature and polarisation anisotropies in the cosmic microwave background radiation due to quantum fluctuations during inflation. Fitting observations of the anisotropies with theoretical realisations obtained by varying various parameters of the curvature power spectrum and cosmological parameters enables one to obtain the allowed ranges of these parameters. We discuss how to relate these parameters to inflation models which allows one to rule in or out specific models of inflation.Comment: Slightly longer version of a plenary review talk at the XXI DAE-BRNS High Energy Physics Symposium at IIT Guwahati, Dec.8-12, 2014. 14 pages, 7 fig

Weak Lensing Probes of Modified Gravity

We study the effect of modifications to General Relativity on large scale weak lensing observables. In particular, we consider three modified gravity scenarios: f(R) gravity, the DGP model, and TeVeS theory. Weak lensing is sensitive to the growth of structure and the relation between matter and gravitational potentials, both of which will in general be affected by modified gravity. Restricting ourselves to linear scales, we compare the predictions for galaxy-shear and shear-shear correlations of each modified gravity cosmology to those of an effective Dark Energy cosmology with the same expansion history. In this way, the effects of modified gravity on the growth of perturbations are separated from the expansion history. We also propose a test which isolates the matter-potential relation from the growth factor and matter power spectrum. For all three modified gravity models, the predictions for galaxy and shear correlations will be discernible from those of Dark Energy with very high significance in future weak lensing surveys. Furthermore, each model predicts a measurably distinct scale dependence and redshift evolution of galaxy and shear correlations, which can be traced back to the physical foundations of each model. We show that the signal-to-noise for detecting signatures of modified gravity is much higher for weak lensing observables as compared to the ISW effect, measured via the galaxy-CMB cross-correlation.Comment: 16 pages, 8 figures; accepted for publication in Phys. Rev. D; v2: references added; v3: clarifications and additions to the text in response to refere

The Small-Scale Power Spectrum of Cold Dark Matter

One of the best motivated hypotheses in cosmology states that most of the matter in the universe is in the form of weakly-interacting massive particles that decoupled early in the history of the universe and cooled adiabatically to an extremely low temperature. Nevertheless, the finite temperature and horizon scales at which these particles decoupled imprint generic signatures on their small scales density fluctuations. We show that the previously recognized cut-off in the fluctuation power-spectrum due to free-streaming of particles at the thermal speed of decoupling, is supplemented by acoustic oscillations owing to the initial coupling between the cold dark matter (CDM) and the radiation field. The power-spectrum oscillations appear on the scale of the horizon at thermal decoupling which corresponds to a mass scale of \~10^{-4}*(T_d/10MeV)^{-3} solar masses for a CDM decoupling temperature T_d. The suppression of the power-spectrum on smaller scales by the acoustic oscillations is physically independent from the free-streaming effect, although the two cut-off scales are coincidentally comparable for T_d~10MeV and a particle mass of M~100GeV. The initial conditions for recent numerical simulations of the earliest and smallest objects to have formed in the universe, need to be modified accordingly. The smallest dark matter clumps may be detectable through gamma-ray production from particle annihilation, through fluctuations in the event rate of direct detection experiments, or through their tidal gravitational effect on wide orbits of objects near the outer edge of the solar system.Comment: Physical Review D, in pres

Cosmic Neutrino Last Scattering Surface

Neutrinos decoupled from the rest of the cosmic plasma when the Universe was less than one second old, far earlier than the photons which decoupled at t=380,000 years. Surprisingly, though, the last scattering surface of the neutrinos is much closer to us than that of the photons. Here we calculate the properties of the last scattering surfaces of the three species of neutrinos.Comment: Important reference to earlier work of Bisnovatyi-Kogan and Seidov added, and mis-spelling of Opher reference correcte

Is a Massive Tau Neutrino Just What Cold Dark Matter Needs?

The cold dark matter (CDM) scenario for structure formation in the Universe is very attractive and has many successes; however, when its spectrum of density perturbations is normalized to the COBE anisotropy measurement the level of inhomogeneity predicted on small scales is too large. This can be remedied by a tau neutrino of mass 1\MeV - 10\MeV and lifetime $0.1\sec - 100\sec$ whose decay products include electron neutrinos because it allows the total energy density in relativistic particles to be doubled without interfering with nucleosynthesis. The anisotropies predicted on the degree scale for ``$\tau$CDM'' are larger than standard CDM. Experiments at $e^\pm$ colliders may be able to probe such a mass range.Comment: 9 pages LaTeX plus 4 figures (available upon request) FERMILAB--Pub--94/026-

Primordial Power Spectra from Anisotropic Inflation

We examine cosmological perturbations in a dynamical theory of inflation in which an Abelian gauge field couples directly to the inflaton, breaking conformal invariance. When the coupling between the gauge field and the inflaton takes a specific form, inflation becomes anisotropic and anisotropy can persist throughout inflation, avoiding Wald's no-hair theorem. After discussing scenarios in which anisotropy can persist during inflation, we calculate the dominant effects of a small persistent anisotropy on the primordial gravitational wave and curvature perturbation power spectra using the "in-in" formalism of perturbation theory. We find that the primordial power spectra of cosmological perturbations gain significant direction dependence and that the fractional direction dependence of the tensor power spectrum is suppressed in comparison to that of the scalar power spectrum.Comment: 25 pages, 2 figures; References added, typos corrected and some discussion expanded; version submitted for publication in PR

The Big Bang and Inflation United by an Analytic Solution

Exact analytic solutions for a class of scalar-tensor gravity theories with a hyperbolic scalar potential are presented. Using an exact solution we have successfully constructed a model of inflation that produces the spectral index, the running of the spectral index and the amplitude of scalar perturbations within the constraints given by the WMAP 7 years data. The model simultaneously describes the Big Bang and inflation connected by a specific time delay between them so that these two events are regarded as dependent on each other. In solving the Fridemann equations, we have utilized an essential Weyl symmetry of our theory in 3+1 dimensions which is a predicted remaining symmetry of 2T-physics field theory in 4+2 dimensions. This led to a new method of obtaining analytic solutions in 1T field theory which could in principle be used to solve more complicated theories with more scalar fields. Some additional distinguishing properties of the solution includes the fact that there are early periods of time when the slow roll approximation is not valid. Furthermore, the inflaton does not decrease monotonically with time, rather it oscillates around the potential minimum while settling down, unlike the slow roll approximation. While the model we used for illustration purposes is realistic in most respects, it lacks a mechanism for stopping inflation. The technique of obtaining analytic solutions opens a new window for studying inflation, and other applications, more precisely than using approximations.Comment: V2 improve computation with better agreement with WMAP 7 years data, and also point out an exact solution for cyclic cosmolog