# On the space of solutions of the Horava theory at the kinetic-conformal point

## TL;DR

This paper explores the solution space of the nonprojectable Horava theory at the kinetic-conformal point, revealing an expanded set of solutions in the Hamiltonian formalism compared to the Lagrangian approach, with implications for cosmology.

## Contribution

It demonstrates that the Hamiltonian formalism admits solutions not present in the Lagrangian formalism due to specific configurations of Lagrange multipliers.

## Key findings

- Hamiltonian formalism has a larger solution space.
- Certain solutions with Lagrange multipliers are absent in the Lagrangian approach.
- Potential for new cosmological solutions in the Hamiltonian framework.

## Abstract

The nonprojectable Horava theory at the kinetic-conformal point is defined by setting a specific value of the coupling constant of the kinetic term of the Lagrangian. This formulation has two additional second class-constraints that eliminate the extra mode. We show that the space of solutions of this theory in the Hamiltonian formalism is bigger than the space of solutions in the original Lagrangian formalism. In the Hamiltonian formalism there are certain configurations for the Lagrange multupliers that lead to solutions that cannot be found in the original Lagrangian formulation. We show specific examples in vacuum and with a source. The solution with the source has homogeneous and isotropic spatial hypersurfaces. The enhancement of the space of solutions leaves the possibility that new solutions applicable to cosmology, or to other physical systems, can be found in the Hamiltonian formalism.