1. General, single field Inflation
Nishant Agarwal
Cornell University

2. Outline Introduction The Hubble flow formalism
Inflation
Observational constraints
Action reconstruction
The Hubble flow formalism
Observable predictions of inflation
Summary and Discussion

3. Introduction Inflation Rapid expansion of the early universe
Solves horizon problem, flatness problem, structure formation, density of magnetic monopoles
Lacks a firm physical basis
Will provide an understanding of particle physics at high energies, maybe string theory

4. Observational constraints
Data from CMB anisotropies and Large scale structure surveys characterize the primordial power spectrum to fine detail
Reconstruct underlying theory from data
DBI inflation, k-inflation
Entire inflaton action instead of just the potential or a specific kinetic term
H. Peiris and R. Easther, JCAP 0607, 002 (2006), astro-ph/
B.A. Powell and W.H. Kinney, JCAP 0708, 006 (2007), arXiv:
J. Lesgourgues, A.A. Starobinsky, and W. Valkenburg, JCAP 0801, 010 (2008), arXiv:

5. Action reconstruction
Include possibility of non-minimal kinetic terms
Can produce large non-Gaussian behaviour for curvature perturbations
General lagrangian, , of a single scalar field , with
In the usual formalism, can be used to reconstruct on fixing a reheating scenario
Now we need a continuous set of independent data analogous to
R. Bean, D.J.H. Chung, and G. Geshnizjiani (2008), arXiv:

6. The Hubble flow formalism
Evolution of the Hubble parameter, , and sound speed for propagation of inhomogeneities, , can be written as an infinite hierarchy of flow parameters.
In the usual gauge ,

7. Essentially we are doing a Taylor expansion in
and .
Acceleration equation,
Scalar and tensor power spectrum:
Power spectra should be evaluated by integrating the equations for scalar and tensor perturbations until the power spectrum freezes out.

8. Observables:
where and

9. Observable predictions of inflation
Flow parameters are constrained using data typically under 2 conditions:
- at horizon crossing, with no condition on the end of inflation
- inflation ends when , and observable scales cross the horizon at a number of e-foldings,

10. Monte-Carlo results with end of inflation imposed
Canonical
inflation
General
inflation
Canonical models earlier investigated in: W.H. Kinney, Phys. Rev. D. 66, (2002), astro-ph/

11. Important differences between general and canonical inflation

12. No multiple horizon crossing

13. Monte-Carlo Markov chain results with no end of inflation imposed (parameters set at horizon crossing)
Canonical
inflation

14. C1 C2

15. General
inflation

16. Work in progress …

17. Summary and Discussion
Hubble flow formalism can be used to reconstruct general inflation as well as canonical inflation
Full integration of the perturbations is useful to get observed scalar and tensor power spectrum
Comparison with CMB+LSS observations gives constraints on the general inflationary action
Allows the prospect that we will learn more about inflation than just potential reconstruction