Exact inflationary solutions in exponential gravity

We consider a modified gravity model of the form $f(R,\phi)=R e^{h(\phi)R}$, where the strong gravity corrections are taken to all orders and $\phi$ is a self-interacting massless scalar field. We show that the conformal transformation of this model to Einstein frame leads to non-canonical kinetic term and negates the advantage of the Einstein frame. We obtain exact solutions for the background in the Jordan frame without performing conformal transformations and show that the model leads to inflation with exit. We obtain scalar and tensor power-spectrum in Jordan frame and show that the model leads to red-tilt. We discuss the implications of the same in the light of cosmological observations.Comment: 17 pages, 4 figures, 2 table

Inflation with f(R,ϕ)f(R,\phi) in Jordan frame

We consider an $f(R)$ action that is non-minimally coupled to a massive scalar field. The model closely resembles scalar-tensor theory and by conformal transformation can be transformed to Einstein frame. To avoid the ambiguity of the frame dependence, we obtain an exact analytical solution in Jordan frame and show that the model leads to a period of accelerated expansion with an exit. Further, we compute the scalar and tensor power spectrum for the model and compare them with observations.Comment: 10 pages, 3 figure

Is there an imprint of Planck scale physics on inflationary cosmology?

We study the effects of the trans-Planckian dispersion relation on the spectrum of the primordial density perturbations during inflation. In contrast to the earlier analyses, we do not assume any specific form of the dispersion relation and allow the initial state of the field to be arbitrary. We obtain the spectrum of vacuum fluctuations of the quantum field by considering a scalar field satisfying the linear wave equation with higher spatial derivative terms propagating in the de Sitter space-time. We show that the power spectrum does not strongly depend on the dispersion relation and that the form of the dispersion relation does not play a significant role in obtaining the corrections to the scale invariant spectrum. We also show that the signatures of the deviations from the flat scale-invariant spectrum from the CMBR observations due to quantum gravitational effects cannot be differentiated from the standard inflationary scenario with an arbitrary initial state.Comment: 6 pages, uses RevTex4; References added; Final versio

A test of Einstein's equivalence principle in future VLBI observations

We show that very-long-baseline-interferometry (VLBI) observations of supermassive black holes will allow us to test the fundamental principles of General Relativity (GR). GR is based on the universality of gravity and Einstein's equivalence principle (EEP). However, EEP is not a basic principle of physics but an empirical fact. Non-minimal coupling (NMC) of electromagnetic fields violates EEP, and their effects manifest in the strong-gravity regime. Hence, VLBI observations of black holes provide an opportunity to test NMC in the strong-gravity regime. To the leading order in the spin parameter, we explicitly show that the NMC of the electromagnetic field introduces observable modifications to the black hole image. In addition, we find that the size of the photon rings varies by $\sim 3 r_H$, which corresponds to $\sim 30 \mu as$ for Sagittarius $A^*$ and $\sim 23 \mu as$ for M87. VLBI telescopes are expected to attain a resolution of $\sim 5 \mu as$ in the near future. However, direct detection of photon ring will require the resolution of $\sim 1 \mu as$ for M87, which can potentially be probed by the space-based Event Horizon Explorer.Comment: V2: Version accepted in PRD Letters. Results are now compared for many VLBI experiments; hence, the title and abstract are modified. 11 Pages, 7 figures (including supplementary material

Probing the BLR in AGNs using time variability of associated absorption line

It is know that most of the clouds producing associated absorption in the spectra of AGNs and quasars do not completely cover the background source (continuum + broad emission line region, BLR). We note that the covering factor derived for the absorption is the fraction of photons occulted by the absorbing clouds, and is not necessarily the same as the fractional area covered. We show that the variability in absorption lines can be produced by the changes in the covering factor caused by the variation in the continuum and the finite light travel time across the BLR. We discuss how such a variability can be distinguished from the variability caused by other effects and how one can use the variability in the covering factor to probe the BLR.Comment: 12 pages, latex(aaspp4.sty), 2 figures, (To appear in ApJ

Non-singular black-holes on the brane

We investigate the possibility of obtaining non-singular black-hole solutions in the brane world model by solving the effective field equations for the induced metric on the brane. The Reissner-Nordstrom solution on the brane was obtained by Dadhich etal by imposing the null energy condition on the 3-brane for a bulk having non zero Weyl curvature. In this work, we relax the condition of vanishing scalar curvature $R$, however, retaining the null condition. We have shown that it is possible to obtain class of static non-singular spherically symmetric brane space-times admitting horizon. We obtain one such class of solution which is a regular version of the Reissner-Nordstrom solution in the standard general relativity.Comment: 8 pages, References added, Version to appear in Int. J. Mod. Phys.

Entanglement as a source of black hole entropy

We review aspects of black hole thermodynamics, and show how entanglement of a quantum field between the inside and outside of a horizon can account for the area-proportionality of black hole entropy, provided the field is in its ground state. We show that the result continues to hold for Coherent States and Squeezed States, while for Excited States, the entropy scales as a power of area less than unity. We also identify location of the degrees of freedom which give rise to the above entropy.Comment: 12 pages, latex, 5 figures. Invited talk by SD at `Recent Developments in Gravity' (NEB XII), Nafplion, Greece, 30 June 2006. To appear in Journal of Physics: Conference Series; V2: References added, Minor changes to match published versio

Method of complex paths and general covariance of Hawking radiation

We apply the technique of complex paths to obtain Hawking radiation in different coordinate representations of the Schwarzschild space-time. The coordinate representations we consider do not possess a singularity at the horizon unlike the standard Schwarzschild coordinate. However, the event horizon manifests itself as a singularity in the expression for the semi-classical action. This singularity is regularized by using the method of complex paths and we find that Hawking radiation is recovered in these coordinates indicating the covariance of Hawking radiation. This also shows that there is no correspondence between the particles detected by the model detector and the particle spectrum obtained by the quantum field theoretic analysis -- a result known in other contexts as well.Comment: 9 pages, uses MPLA Style file, Accepted for publication in Mod. Phys. Letts.