In recent years, theories in which the Einstein-Hilbert Lagrangian is replaced by a function

Attempts to modify the theory of general relativity, by including higher-order invariants in the action, started not too long after its inception [

Now in another direction, the quest for quantum theory of gravity has led to the study of the simpler case of gravitational theory in two-dimensional spacetime. Such a spacetime provides an interesting arena in which to explore some fundamental aspects of both classical and quantum gravity. The reduction in the degrees of freedom greatly simplifies the analysis of the field equations. This leads to appreciable understanding of several problems in gravity theory. In two-dimensional spacetime, the two-dimensional gravitational constant

In Section

We write the two-dimensional action for

In this section we seek solutions of the cosmological field equation (

For the radiation dominated epoch the corresponding equations read

Ideally one should solve (

Next we substitute (

We now turn to the case of radiation. Upon adding (

We now discuss some properties of the solutions of the cosmological field equations found in the previous section. Let us first look at the radiation dominated case and determine whether our vision of the universe is limited by a particle horizon. At a given cosmic time

Next we turn to the case of the matter dominated universe described by (

We now consider the case

It is clear that the integral converges for

Next we consider the behavior of

The horizon problem in four-dimensional standard FRW cosmology is a consequence of deceleration in the expansion of the universe. The problem can be solved by postulating a phase of the universe, prior to the decelerating phase, in which the expansion is accelerating and such a phase is called a period of inflation. Hence inflation is characterized by the following property for the scale factor

As in four spacetime dimensions we define the so-called slow-roll parameter

We shall next seek a general solution to (

We write

Substituting (

The Hubble parameter is given by

It thus decreases from an initial value

to a value

The number of

As we stated in the introduction two-dimensional spacetime models of gravity provide an arena where issues like quantization are studied since in such a setting they prove to be more tractable than in four-dimensional spacetime. In this section we thus consider quantization of the

take

fact one can easily derive that

Equation (

n:

In this work we studied

Now as we mentioned before, the interest behind the pursuit of

Interest in two-dimensional theories stems partially from the desire to investigate the quantum theory in a simple setting. Hence we carried out quantization of the theory in the case of