How to measure redshift-space distortions without sample variance

We show how to use multiple tracers of large-scale density with different biases to measure the redshift-space distortion parameter beta=f/b=(dlnD/dlna)/b (where D is the growth rate and a the expansion factor), to a much better precision than one could achieve with a single tracer, to an arbitrary precision in the low noise limit. In combination with the power spectrum of the tracers this allows a much more precise measurement of the bias-free velocity divergence power spectrum, f^2 P_m - in fact, in the low noise limit f^2 P_m can be measured as well as would be possible if velocity divergence was observed directly, with rms improvement factor ~[5.2(beta^2+2 beta+2)/beta^2]^0.5 (e.g., ~10 times better than a single tracer for beta=0.4). This would allow a high precision determination of f D as a function of redshift with an error as low as 0.1%. We find up to two orders of magnitude improvement in Figure of Merit for the Dark Energy equation of state relative to Stage II, a factor of several better than other proposed Stage IV Dark Energy surveys. The ratio b_2/b_1 will be determined with an even greater precision than beta, producing, when measured as a function of scale, an exquisitely sensitive probe of the onset of non-linear bias. We also extend in more detail previous work on the use of the same technique to measure non-Gaussianity. Currently planned redshift surveys are typically designed with signal to noise of unity on scales of interest, and are not optimized for this technique. Our results suggest that this strategy may need to be revisited as there are large gains to be achieved from surveys with higher number densities of galaxies.Comment: 22 pages, 13 figure

Gravitational lensing as a contaminant of the gravity wave signal in CMB

Gravity waves (GW) in the early universe generate B-type polarization in the cosmic microwave background (CMB), which can be used as a direct way to measure the energy scale of inflation. Gravitational lensing contaminates the GW signal by converting the dominant E polarization into B polarization. By reconstructing the lensing potential from CMB itself one can decontaminate the B mode induced by lensing. We present results of numerical simulations of B mode delensing using quadratic and iterative maximum-likelihood lensing reconstruction methods as a function of detector noise and beam. In our simulations we find the quadratic method can reduce the lensing B noise power by up to a factor of 7, close to the no noise limit. In contrast, the iterative method shows significant improvements even at the lowest noise levels we tested. We demonstrate explicitly that with this method at least a factor of 40 noise power reduction in lensing induced B power is possible, suggesting that T/S=10^-6 may be achievable in the absence of sky cuts, foregrounds, and instrumental systematics. While we do not find any fundamental lower limit due to lensing, we find that for high-sensitivity detectors residual lensing noise dominates over the detector noise.Comment: 6 pages, 2 figures, submitted to PR

Cosmology from Moduli Dynamics

We investigate moduli field dynamics in supergravity/M-theory like set ups where we turn on fluxes along some or all of the extra dimensions. As has been argued in the context of string theory, we observe that the fluxes tend to stabilize the squashing (or shape) modes. Generically we find that at late times the shape is frozen while the radion evolves as a quintessence field. At earlier times we have a phase of radiation domination where both the volume and the shape moduli are slowly evolving. However, depending on the initial conditions and the parameters of the theory, like the value of the fluxes, curvature of the internal manifold and so on, the dynamics of the internal manifold can be richer with interesting cosmological consequences, including inflation.Comment: 38 pages, 6 figures; references adde

Cosmic Acceleration in Brans-Dicke Cosmology

We consider Brans-Dicke theory with a self-interacting potential in Einstein conformal frame. We show that an accelerating expansion is possible in a spatially flat universe for large values of the Brans-Dicke parameter consistent with local gravity experiments.Comment: 10 Pages, 3 figures, To appear in General Relativity and Gravitatio

A Space-Time Orbifold: A Toy Model for a Cosmological Singularity

We explore bosonic strings and Type II superstrings in the simplest time dependent backgrounds, namely orbifolds of Minkowski space by time reversal and some spatial reflections. We show that there are no negative norm physical excitations. However, the contributions of negative norm virtual states to quantum loops do not cancel, showing that a ghost-free gauge cannot be chosen. The spectrum includes a twisted sector, with strings confined to a ``conical'' singularity which is localized in time. Since these localized strings are not visible to asymptotic observers, interesting issues arise regarding unitarity of the S-matrix for scattering of propagating states. The partition function of our model is modular invariant, and for the superstring, the zero momentum dilaton tadpole vanishes. Many of the issues we study will be generic to time-dependent cosmological backgrounds with singularities localized in time, and we derive some general lessons about quantizing strings on such spaces.Comment: 21 pages, 2 figure

Fundamental constants and tests of general relativity - Theoretical and cosmological considerations

The tests of the constancy of the fundamental constants are tests of the local position invariance and thus of the equivalence principle. We summarize the various constraints that have been obtained and then describe the connection between varying constants and extensions of general relativity. To finish, we discuss the link with cosmology, and more particularly with the acceleration of the Universe. We take the opportunity to summarize various possibilities to test general relativity (but also the Copernican principle) on cosmological scales.Comment: Proceedings of the workshop ``The nature of gravity, confronting theory and experiment in space'', ISSI, Bern, october 200

Interacting Open Wilson Lines in Noncommutative Field Theories

In noncommutative field theories, it was known that one-loop effective action describes propagation of non-interacting open Wilson lines, obeying the flying dipole's relation. We show that two-loop effective action describes cubic interaction among `closed string' states created by open Wilson lines. Taking d-dimensional noncommutative [\Phi^3] theory as the simplest setup, we compute nonplanar contribution at low-energy and large noncommutativity limit. We find that the contribution is expressible in a remarkably simple cubic interaction involving scalar open Wilson lines only and nothing else. We show that the interaction is purely geometrical and noncommutative in nature, depending only on sizes of each open Wilson line.Comment: v1: 27 pages, Latex, 7 .eps figures v2: minor wording change + reference adde

Schwarzschild black hole surrounded by quintessence: Null geodesics

We have studied the null geodesics of the Schwarzschild black hole surrounded by quintessence matter. Quintessence matter is a candidate for dark energy. Here, we have done a detailed analysis of the geodesics and exact solutions are presented in terms of Jacobi-elliptic integrals for all possible energy and angular momentum of the photons. The circular orbits of the photons are studied in detail. As an application of the null geodesics, the angle of deflection of the photons are computed.Comment: 25 pages, 20 figures. typos corrected and some of the notation change

Signatures of very high energy physics in the squeezed limit of the bispectrum (violation of Maldacena's condition)

We investigate the signatures in the squeezed limit of the primordial scalar bispectrum due to modifications of the standard theory at high energy. In particular, we consider the cases of modified dispersion relations and/or modified initial quantum state (both in the Boundary Effective Field Theory and in the New Physics Hyper-Surface formulations). Using the in-in formalism we study in details the squeezed limit of the contributions to the bispectrum from all possible cubic couplings in the effective theory of single-field inflation. We find general features such as enhancements and/or non-local shape of the non-Gaussianities, which are relevant, for example, for measurements of the halo bias and which distinguish these scenarios from the standard one (with Bunch-Davies vacuum as initial state and standard kinetic terms). We find that the signatures change according to the magnitude of the scale of new physics, and therefore several pieces of information regarding high energy physics could be obtained in case of detection of these signals, especially bounds on the scales of new physics.Comment: 37 pages plus bibliography, version matching the one accepted for publication by JCAP. Increased pedagogical comments, improved presentation and text, added reference

What we don't know about time

String theory has transformed our understanding of geometry, topology and spacetime. Thus, for this special issue of Foundations of Physics commemorating "Forty Years of String Theory", it seems appropriate to step back and ask what we do not understand. As I will discuss, time remains the least understood concept in physical theory. While we have made significant progress in understanding space, our understanding of time has not progressed much beyond the level of a century ago when Einstein introduced the idea of space-time as a combined entity. Thus, I will raise a series of open questions about time, and will review some of the progress that has been made as a roadmap for the future.Comment: 15 pages; Essay for a special issue of Foundations of Physics commemorating "Forty years of string theory