Can non-local or higher derivative theories provide alternatives to inflation?

Abstract

The standard mechanism for producing the observed scale-invariant power spectrum from adiabatic vacuum fluctuations relies on first order derivative of fields in the action for curvature perturbations. It has been proven \cite{Geshnizjani:2011dk} that, under this ansatz, any theory of early universe that matches cosmological observations should include a phase of accelerated expansion (i.e. inflation) or it has to break at least one of the following tenets of classical general relativity: Null Energy Conditions (NEC), subluminal signal propagation, or sub-Planckian energy densities. We extend this proof to a large class of theories with higher (spatial) derivative or non-local terms in the action. Interestingly, only theories in the neighborhood of Lifshitz points with ${\omega }_k\propto k^0$ and $k^3$ remain viable.

27 pages, 3 figures, added some references. corrected few typos, matches the published version in JCAP

References in corpus (8)

• Quantum Gravity at a Lifshitz Point
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Galilean Genesis: an alternative to inflation
• Speedy sound and cosmic structure
• Generalized Slow Roll for Non-Canonical Kinetic Terms
• Reconstructing a general inflationary action
• Generating Scale-Invariant Perturbations from Rapidly-Evolving Equation of State
• Seeding of Primordial Perturbations During a Decelerated Expansion

Cited by in corpus (6)

• Spectrum of Cuscuton Bounce
• Non-Gaussian signatures of general inflationary trajectories
• Theoretical implications of detecting gravitational waves
• Consistency of Tachyacoustic Cosmology with de Sitter Swampland Conjectures
• Cuscuton Bounce Beyond the Linear Regime: Bispectrum and Strong Coupling Constraints
• The Trans-Planckian problem in Tachyacoustic Cosmology