Granting that time travel would ever be conceivable, I would make the following comments:
Initially a reason should be provided to suggest that something is assur. Coincidentally however, I have thought of a comparable precedent which demonstrates how it is permissible to travel through time.
Whenever we move, we inevitably alter time imperceptibly because of time dilation, according to the theory of relativity. And there is no halacha issue with movement, so it follows that there is no halacha issue of altering time. Perhaps according to the same logic, altering your position in time in the backward direction would not be a problem.
However, another issue can be at play. If one travels gradually backward in a machine of sorts and passes through the time of Shabbat or Yom Tov, it would seem that the familiar issues with operating machinery on these days would apply, even though one would be moving backward in time. If one could somehow skip from one moment to another though, he/she may be able to circumvent this problem.
The Talmud in Tractate Menachot (29b) says Moshe Rabeinu was transported in time to Rabbi Akiva's torah class and couldn't follow it.
The mishna in Chagigah (2:1) mentions some things which man cannot delve into:
וכל המסתכל בארבעה דברים, ראוי לו כאילו לא בא לעולם--מה למעלה, מה למטה, מה לפנים, מה לאחור. וכל שלא חס על כבוד קונו, ראוי לו כאילו לא בא לעולם.
" Whoever looks at four things, it would have been better for him if he had never come into the world: 1) what is above [the sky], 2) what is below [the earth], 3) what was before [the Creation] and 4) what will be after [in the end of days]. And whoever takes no account of the honor of his Maker [see the following section in the Gemara], it would have been better for him if he had never come into the world."
These appear to refer to Hashem's realm of space ('above' and 'below') and time ('before' and 'after'). There are those things which are inherently incomprehensible to us. Although this isn't directly related to time travel, it Bartenura writes how it related to unknowable epochs:
מה לפנים? קודם שנברא העולם. מה לאחור? בסוף העולם לאחרית הימים.
According to the Bartenura knowledge of 'pre-Earth' as well as 'acharit hayamim' (a specific point in time in the future) would be problematic.
The Kehati gives further explanation:
ולכן אסור לו לחקור בהם, כי עלול הוא לבוא לידי טעויות ולידי מבוכה בענייני האמונה
Having said all this, this is in reference to learning about these topics. Perhaps this idea can be extrapolated by a kal v'chomer.