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We explore the effects of size of the box that we use for simulations of the intergalactic medium (IGM) at redshift 2. We examine simulations from the hydrodynamic code  enzo  that differ only in box size. We study the cold dark matter (CDM) distribution and many statistics of the Lyα forest absorption from the IGM. Larger boxes have fewer pixels with significant absorption (flux &lt;0.96), more pixels in longer stretches with little or no absorption, and they have wider Lyα lines. The larger boxes differ only because they include power from longer wavelength modes. These modes result in higher peak densities, higher velocities and hotter gas. Small simulations are too cold compared to larger ones. When we deliberately increase the heat we put into the IGM, we can approximate the Lyα forest in a simulation of twice the size.  When we double the box size, the difference of most statistics from their value in our largest 76.8 Mpc box is reduced by approximately a factor of 2. When we enlarge the box from 38.4 to 76.8 Mpc, the mean Lyα absorption decreases 0.5 per cent, the frequency with which we encounter different common CDM densities changes by 2 per cent, typical Lyα linewidths, the frequency of flux values and the power spectrum of the flux all change by 4–7 per cent, and the column density distribution changes by up to 15 per cent. A 76.8 Mpc box is large enough to give errors of &lt;1 per cent for the mean flux, 5 per cent for the column density distribution and power spectrum and 5–10 per cent for the flux distribution. When we compare to the errors in data, we find that our 76.8 Mpc box is larger than we need for the mean flux, barely large enough for the flux distribution, column density distribution and the power spectrum of the flux, and too small for the linewidths. Cells of size 18.75 kpc are small enough to give errors of &lt;1 per cent for the mean flux, 1–5 per cent for linewidths, 5 per cent for the column densities and power and 5–10 per cent for the flux distribution. Compared to data, the simulated spectra in our largest box differ from data in all statistics, except, by design, the mean flux. The simulated spectra have too many Lyα lines with small H  i  column densities  log  N  H  i   &lt; 14 cm −2  , and too few with larger  log  N  H  i    values. They have factors of 3–30 times too few lines with  &gt;10 17  cm −2  . Decreasing the cell size from 75 to 18.75 kpc makes the difference larger at  log  N  H  i   &lt; 14 cm −2  , and does not help with the higher columns. The Lyα lines in the simulated spectra from a very large box with 18.75 kpc cells would be too wide by 2.6 km s −1 . The simulated Lyα forest has 20 per cent too little power on small scales and 50 per cent too little large scales. A much larger box would increase the large‐scale power only a few per cent. We confirm the Kim et al. (2007) and Bolton et al. (2008) finding that the simulated spectra also have different flux distributions than data.  It is hard to see how our optically thin simulations using popular cosmological and astrophysical parameters can match the Lyα forest data at   z = 2 . Adding radiation transfer effects, especially shelf‐shielding will reduce the temperature at high overdensities, possibly improving the match to linewidths, and it will help match the number of high column density lines. We could also decrease the linewidths with a softer ionizing spectrum, or by using  σ 8  &gt; 0.9 , which has the additional benefit of increasing the large‐scale power.

The effect of large‐scale power on simulated spectra of the Lyα forest