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

Phenomenology of the CAH+ measure

The CAH+ measure regulates the infinite spacetime volume of the multiverse by constructing a surface of constant comoving apparent horizon (CAH) and then removing the future lightcones of all points on that surface (the latter prescription is referred to by the "+" in the name of the measure). This measure was motivated by the conjectured duality between the bulk of the multiverse and its future infinity and by the causality condition, requiring that the cutoff surfaces of the measure should be spacelike or null. Here we investigate the phenomenology of the CAH+ measure and find that it does not suffer from any known pathologies. The distribution for the cosmological constant Lambda derived from this measure is in a good agreement with the observed value, and the distribution for the number of inflationary e-foldings satisfies the observational constraint. The CAH+ measure does not exhibit any "runaway" behaviors at zero or negative values of Lambda, which have been recently shown to afflict a number of other measures.Comment: 35 pages, including 6 figures and 2 appendices; v2 corrections in Section 2.4, conclusions unchange

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-

Neutrino Mass and Dark Energy from Weak Lensing

Weak gravitational lensing of background galaxies by intervening matter directly probes the mass distribution in the universe. This distribution, and its evolution at late times, is sensitive to both the dark energy, a negative pressure energy density component, and neutrino mass. We examine the potential of lensing experiments to measure features of both simultaneously. Focusing on the radial information contained in a future deep 4000 square degree survey, we find that the expected (1-sigma) error on a neutrino mass is 0.1 eV, if the dark energy parameters are allowed to vary. The constraints on dark energy parameters are similarly restrictive, with errors on w of 0.09. Much of the restrictive power on the dark energy comes not from the evolution of the gravitational potential but rather from how distances vary as a function of redshift in different cosmologies