From Wave Geometry to Fake Supergravity

The `Wave Geometry' equation of the pre-WWII Hiroshima program is also the key equation of the current `fake supergravity' program. I review the status of (fake) supersymmetric domain walls and (fake) pseudo-supersymmetric cosmologies. An extension of the domain-wall/cosmology correspondence to a triple correspondence with instantons shows that `pseudo-supersymmetry' has another interpretation as Euclidean supersymmetry.Comment: 14 pages. Minor Revisions to original. To appear in proceedings of the 5th International Symposium on Quantum Theory and Symmetries (QTS5), Vallodolid, July 2007. in version

Constraining Inflation

Slow roll reconstruction is derived from the Hamilton-Jacobi formulation of inflationary dynamics. It automatically includes information from sub-leading terms in slow roll, and facilitatesthe inclusion of priors based on the duration on inflation. We show that at low inflationary scales the Hamilton-Jacobi equations simplify considerably. We provide a new classification scheme for inflationary models, based solely on the number of parameters needed to specify the potential, and provide forecasts for likely bounds on the slow roll parameters from future datasets. A minimal running of the spectral index, induced solely by the first two slow roll parameters (\epsilon and \eta) appears to be effectively undetectable by realistic Cosmic Microwave Background experiments. However, we show that the ability to detect this signal increases with the lever arm in comoving wavenumber, and we conjecture that high redshift 21 cm data may allow tests of second order consistency conditions on inflation. Finally, we point out that the second order corrections to the spectral index are correlated with the inflationary scale, and thus the amplitude of the CMB B-mode.Comment: 32 pages. v

Inflation and Quintessence: Theoretical Approach of Cosmological Reconstruction

In the first part of this paper, we outline the construction of an inflationary cosmology in the framework where inflation is described by a universally evolving scalar field, with the Lagrangian ${\cal L}_\phi=-{1/2}(\partial\phi)^2 -V(\phi)$. By considering a generic situation that inflaton attains a nearly constant velocity, during inflation, $m_P^{-1} (d\phi/dN)\equiv \alpha$ (where $N\equiv \ln a$ is the e-folding time), we find the conditions that have to satisfied by the (reconstructed) scalar potential to be consistent with the WMAP inflationary data. In the second part of this paper, we introduce a novel approach of constructing dark energy within the context of the standard scalar-tensor gravity. The assumption that a scalar field might roll with a nearly constant velocity, during inflation, can also be applied to {\it quintessence} or dark energy models. For the minimally coupled quintessence, $\alpha_Q\equiv dA(Q)/d(\kappa Q)=0$ (where $A(Q)$ is the standard matter-quintessence coupling), the dark energy equation of state in the range $-1\le w_{DE} < -0.82$ can be obtained for $0\le \alpha < 0.63$. For $\alpha<0.1$, the model allows for only modest evolution of dark energy density with redshift. The effect of the matter-quintessence coupling can be significant only if $|\alpha_Q| \gtrsim 0.1$, while a small coupling $|\alpha_Q|< 0.1$ will have almost no effect on cosmological parameters. The best fit value of $\alpha_Q$ in our model is found to be $\alpha_Q \simeq 0.06$, but it may contain significant numerical errors, viz $\alpha_Q=0.06\pm 0.35$, which thereby implies the consistency of our model with general relativity (for which $\alpha_Q=0$) at $1\sigma$ level.Comment: 33 pages, several figures; significant extension (models confronted with data