118490430
CMB imprints of a pre-inflationary climbing phase
We discuss the implications for cosmic microwave background (CMB) observables, of a class of pre-inflationary dynamics suggested by string models where SUSY is broken due to the presence of D-branes and orientifolds preserving incompatible portions of it. In these models the would-be inflaton is forced to emerge from the initial singularity climbing up a mild exponential potential, until it bounces against a steep exponential potential of ``brane SUSY breaking'' scenarios, and as a result the ensuing descent gives rise to an inflationary epoch that begins when the system is still well off its eventual attractor. If a pre-inflationary climbing phase of this type had occurred within 6-7 e-folds of the horizon exit for the largest observable wavelengths, displacement off the attractor and initial-state effects would conspire to suppress power in the primordial scalar spectrum, enhancing it in the tensor spectrum and typically superposing oscillations on both. We investigate these imprints on CMB observables over a range of parameters, examine their statistical significance, and provide a semi-analytic rationale for our results. It is tempting to ascribe at least part of the large-angle anomalies in the CMB to pre-inflationary dynamics of this type.
119088066
UV/IR mode mixing and the CMB
It is well understood that spatial noncommutativity, if indeed realized in nature, is a phenomenon whose effects are not just felt at energy scales comparable to the noncommutativity scale. Loop effects can transmit signatures of any underlying noncommutativity to macroscopic scales (a manifestation of a phenomenon that has come to be known as UV/IR mode mixing) and offer a potential lever to constrain the amount of noncommutativity present in nature, if present at all. Field theories defined on noncommutative spaces (realized in string theory when D-branes are coupled to backgrounds of nontrivial RR background flux), can exhibit strong UV/IR mode mixing, manifesting in a nonlocal one-loop effective action. In the context of inflation in the presence of any background noncommutativity, we demonstrate how this UV/IR mixing at the loop level can allow us to place severe constraints on the scale of noncommutativity if we presume inflation is responsible for large-scale structure. We demonstrate that any amount of noncommutativity greatly suppresses the cosmic microwave background power at all observable scales, independent of the scale of inflation, and independent of whether or not the noncommutativity tensor redshifts during inflation, therefore nullifying a very salient and successful prediction of inflation.
119275413
On Semi-classical Degravitation and the Cosmological Constant Problems
In this report, we discuss a candidate mechanism through which one might address the various cosmological constant problems. We first observe that the renormalization of gravitational couplings (induced by integrating out various matter fields) manifests non-local modifications to Einstein’s equations as quantum corrected equations of motion. That is, at the loop level, matter sources curvature through a gravitational coupling that is a non-local function of the covariant d’Alembertian. If the functional form of the resulting Newton’s ‘constant’ is such that it annihilates very long wavelength sources, but reduces to 1=M 2 (Mpl being the 4d Planck mass) for all sources with cosmologically observable wavelengths, we would have a complimentary realization of the degravitation paradigm– a realization through which its non-linear completion and the corresponding modified Bianchi identities are readily understood. We proceed to consider various theories whose coupling to gravity may a priori induce non-trivial renormalizations of Newton’s constant in the IR, and arrive at a class of non-local effective actions which yield a suitably degravitating filter function for Newton’s constant upon subsequently being integrated out. We motivate this class of non-local theories through several considerations, discuss open issues, future directions, the inevitable question of scheme dependence in semi-classical gravitational calculations and comment on connections with other meditations in the literature on relaxing of the cosmological constant semi-classically.
119086649
Radion stabilization by stringy effects in general relativity
We consider the effects of a gas of closed strings (treated quantum mechanically) on a background where one dimension is compactified on a circle. After we address the effects of a time-dependent background on aspects of the string spectrum that concern us, we derive the energy-momentum tensor for a string gas and investigate the resulting space-time dynamics. We show that a variety of trajectories are possible for the radius of the compactified dimension, depending on the nature of the string gas, including a demonstration within the context of general relativity (i.e. without a dilaton) of a solution where the radius of the extra dimension oscillates about the self-dual radius, without invoking matter that violates the various energy conditions. In particular, we find that in the case where the string gas is in thermal equilibrium, the radius of the compactified dimension dynamically stabilizes at the self-dual radius, after which a period of usual Friedmann-Robertson-Walker cosmology of the three uncompactified dimensions can set in. We show that our radion stabilization mechanism requires a stringy realization of inflation as scalar field driven inflation invalidates our mechanism. We also show that our stabilization mechanism is consistent with observational bounds.
123359231
ON THE INDEFINITE METRIC.
Abstract We point out: (i) a pseudo-hermitian Hamiltonian has conjugate-energy states if its complex eigenvalues do not belong to the residual spectrum of its adjoint, (ii) particle-antiparticle symmetry puts certain restrictions on the decay channels if there are to be no negative norm, real-energy states, and (iii) exponential time dependence of decays is valid for a pseudo-hermitian Hamiltonian if the initial conditions are chosen with care.
120196663
Dispersion relations for stark energy shifts in hydrogen atom
Abstract On the basis of an approximate but nonperturbative expression for the energy shift δE in the ground state of the hydrogen atom in the presence of an electric field of strength E , we deduce that δE has a branch point at E = 0, and an asymptotic behavior δE → −1 2 E ln E as E → ∞. These properties lead to a twice-subtracted dispersion relation for δE as a function of E . The dispersion relations in conjunction with the WKB approximation and the perturbation series allow us to (i) deduce the large-n behavior of the coefficient of E n in the perturbation series for δE( E ) including 1 n corrections and (ii) obtain the energy shift and the level width of the ground state for a large range of values of E . The agreement with the earlier numerical calculations is very satisfactory.
122881667
Wave functions for weakly coupled bound states
It has been observed' that a short-range attractive potential always produces a bound state in one or two dimensions. This property has been investigated in the weak-coupling limit, with the intention of obtaining perturbative expressions for the bound-state wave functions and energies. In particular, Hausmann has analyzed the bound states in one-dimensional, short-range potentials by using the homogeneous Lippmann-Schwinger equation for the bound-state wave functions. He showed that for the one-dimensional Hamiltonian V(x)~ —ax as x~+ ao, —2
122034057
Ground-state energy of two-dimensional weakly coupled Hamiltonians
It is observed' that a short-range attractive potential always produces a bound state in one or two dimensions. While this property has attracted considerable attention for one-dimensional potentials, leading to many general results, ' ' much less is known about the corresponding property in two dimensions. This may be due to the fact that the bound state is marginal in the case of two dimensions, and somewhat harder to analyze. Apart from the original result of Landau and Lifshitz, ' the only other results known for the two-dimensional problem are those obtained by Simon. ' For the two-dimensional Ham iltonian verse of the T matrix, thus allowing a perturbative description of the poles of the T matrix and hence the bound-state energies. In our present note, the ground-state energy of Hmniltonian (1) is analyzed using the Noyes form' of the T matrix. We find that for potentials satisfying conditions (2) and (3), the ground-state energy has an asymptotic series given by
124903228
Radiative Corrections to K(L) --> mu+ mu-