First I would like to state explicitly several cosmological models which relate to your question:
- Cyclic model
- One-sided infinite linear model with fixed begin and open end
- Two-sided infinite linear model with begin and end open
- Finite linear model with fixed begin and end.
Model 1 occurs in Hindu mythology and in loop quantum cosmology (Bojowald, Martin: Once Before Time: A Whole Story of the Universe. 2010).
Model 2 occurs in the Jewish mythology It is also one of the cosmological standard models. Model 3 is one of the cosmological standard models.
Ad 1. Hindu mythology considers the world as an infinite sequence of creation, existence, and destruction. The model is sometimes illustrated by the cosmic dance of Shiva. Differently, each of the three phases is attributed as a seprate task to the three main gods Brahma (creator), Vishnu (preserver) and Shiva (destroyer).
Model 1 has been picked up as a hypothesis by the German philosopher Friedrich Nietzsche under the title „eternal recurrence” in central parts of his philosophy.
Ad 2. In a religious the model is always combined with a personal creator. The model has been packed up by Christian mythology. In cosmology it is one of the favoured models since the investigation of the accelerated cosmological expansion. The latter is ascribed to the “dark energy”.
Ad 3 and 4. I do not know a representative of this type of model.
Is there a considerable expert bias toward one theory for nontheists, or even certain theists?
Both, a-theists like Nietzsche and theists like Hindus adhere to the cyclic model no. 1. But theists from other religions adhere to the linear model no. 2.
All models leave open the question how and why the world is as it is according to the model. A final question from metaphysics therefore asks „Why is there something rather than nothing?“, see
Where do both the scientific community and philosophical community stand on this issue?
Both models no. 1 and no. 2 are discussed by the scientific community. They are discussed on scientific grounds like the average mass density or the possible existence of dark energy, e.g., see „Part III Spacetime and Cosmology“ in Greene, Brian: The Fabric of the Cosmos. (2004)
I cannot decide whether the philosophical community takes an indenpendent stance to decide between the different models. Eventually, metaphysical discussions on cosmology terminate with the final question cited above.