A new global 1-form in Lyra geometric cosmos model

Dark energy phenomena has inspired lots of investigations on the cosmological constant problems. In order to understand its origin and properties as well as its impacts on universe's evolutions, there are many approaches to modify the well-known General Relativity, such as the Weyl-Lyra Geometry. In the well studied cosmology model within Lyra geometry, there is a problem that the first law of thermodynamics is violated. To unravel this issue, if we use the effective density and pressure in the Lyra cosmology model to preserve the first law of thermodynamics in the cosmos, the former 1-form $(\beta,0,0,0)$ cannot give a proper vacuum behavior. In this paper, the auxiliary 1-form is modified to overcome this difficulty. It can be shown that the complex terms in the field equation derived from the regime of Lyra Geometric$ \frac{3}{2}{\phi}^{\mu}{\phi}_{\nu}-\frac{3}{4}{\delta}^{\mu}_{\nu}{\phi}^{\alpha}{\phi}_{\alpha}$with our new 1-form could behave just as the cosmological constant. This work can be regarded as a new exploration on a possible origin of the cosmological constant from a Lyra cosmology model.