When we say that a star is located 10 billion light years away, it means that the light we receive from that star today has been traveling for approximately 10 billion years to reach us. However, due to the expansion of the universe, the distance between the star and us has also been increasing during that time. This expansion can indeed affect the total time it takes for light to reach us from distant objects.
The expansion of the universe causes space itself to stretch and expand, carrying galaxies and other celestial objects along with it. As a result, the wavelength of light traveling through expanding space gets stretched as well, leading to a phenomenon known as cosmological redshift. This redshift occurs because the expansion of space increases the wavelength of the light, shifting it towards the red end of the electromagnetic spectrum.
So, while the light from a star 10 billion light years away does indeed travel for about 10 billion years, it experiences cosmological redshift along the way due to the expansion of the universe. As a result, the light we observe today from that star has a longer wavelength than when it was emitted, indicating that it has been stretched by the expansion of space.
To calculate the actual time it takes for the light to reach us, considering the expansion of the universe, we need to account for the changing distance between the star and us due to the expansion. This calculation involves factors such as the rate of expansion of the universe, which is described by the Hubble constant. The precise calculation depends on the cosmological model used to describe the expansion of the universe, taking into account factors like dark energy and the curvature of space.
In summary, the light from a star located 10 billion light years away does experience cosmological redshift due to the expansion of the universe. The total time it takes for the light to reach us is influenced by both the distance the light has traveled and the expansion of space along the way. The precise calculation of this time depends on the details of the cosmological model used to describe the universe's expansion.